F1 2013

You really can't make a solution for this achievement, but you can at least make a guideline.

Here are the settings my partner DAN5KI97 and I used:

Participation Level
Short Race Weekend
Short Race Weekend includes the race and one 15 minute qualifying. Originally we had it set to one shot qualifying, but that yielded really poor results. The 15 minutes gives you ample time to learn the track and get a good time as apposed to only one lap. If you and your partner are happy with your times, you don't have to wait the entire 15 minutes. Hit the pause button, go to session options, and select "Vote to skip session." If both players choose this, the game will fast forward to race day

Race Distance
3 Laps
This one's pretty self explanatory. Minimize the time spent on each track; minimize the overall completion time.

AI Difficulty
Amateur
This makes it that much easier to win.

Rules and Flags
Off
Unlike single player, in co-op, you can turn all penalties off. This means you can do whatever you need to do to win. Take out other drivers, cut corners, illegally pass, whatever; You won't get penalized.

Parc Ferme
We left it on, but honestly, this doesn't really matter. Changing the car set up isn't going to really make all that much of a difference considering the other settings.

Car Damage Simulation
Off
Don't want to have to pit for damage in a 3 lap race, do you?

Braking Assist
Low, Lowest, or Off
We discovered that the lower your brake assist setting is, the faster you'll be able to cut corners. When you go off the track, the game tries to slow you down. The higher your brake assist, the more speed you'll lose in the corner cuts. Initially, I had mine on "Medium" while DAN5KI97 had his off. Driving the same lines, he was generally getting qualifying times 5-6 seconds faster. Once I switched to "Low," I'm not skilled enough to turn it off, that gap dropped to about 3 seconds.

If you're not happy with your qualifying times or your race positions, the host can quit to the main menu before you reach the results screen and the progress will not be saved. When relaunching the campaign, it will start at the beginning of whatever session you were on (i.e. If you quit during the race, it will start the race over, not put you back in qualifying).

Also note there seems to be a delay in the unlock. The achievement unlocks as soon as you've reached enough points that your team is unbeatable (there were about 4 or 5 races left for us). DAN5KI97 unlocked it immediately after concluding the race, while I, the host, didn't get it until the loading screen for the next location.

I did this playing as Mercedes Petronas AMG. I ran 3 co-op seasons as Marussia (since they are pretty awful and wouldnt be scoring too many points) and just retired from every race to see who the main competition was. They (Mercedes) were consistently winning the constructor's cup (by 148/23/103 pts respectively). Ferrari and Infiniti were usually fairly close to each other in 2nd/3rd (averaging just under 50pts separation). That doesn't mean Mercedes is the best, but I wanted the other top teams to be fairly evenly matched so I could grab 1st while they battled for 2nd.
This CAN be done "solo" by one person dual boxing. You will need to get 1st almost every time and abuse the competition when possible.
It is much easier with two of course. You could just skip the handful of annoying courses and rack up 33 points on he rest and you will be untouchable.
On the easier courses feel free to turn damage on for the races and do mean, unsportsmanlike things to Ferrari (Alonso/Massa) and Infiniti (Vettel/Webber), as they are your only real competition. If you can keep them out of the three you are pretty much golden. On races where you can catch back up easily, slam on your brake so they rear end you, or slow down enough that they can try to pass and then push them off the road. They will likely never recover their original position. You can also mess them up without damage on, especially on tight tracks like Monaco this may be safer.
If you want to practice a particular section, time attack gives you infinite rewinds to repeat the section you want.

Race Settings
Participation Level: Short Weekend - One-Shot Qualifying
Race Distance: 3 laps

Difficulty Level: (NB: you can change these any time you stop and resume the session. So you can turn damage on on bigger tracks to make it easier to knock people out of the race, and turn it off on street tracks where it is just too dangerous.)
AI Difficulty Level: Amateur
Rules and Flags: Off
Parc Ferme: Off
Car Damage Simulation: See above
Braking Assist: I would turn this off as you will be doing things the AI thinks are nuts, and it will try to brake for you when you don't want it to.
The rest are up to you, but I used:
ABS: On
Traction Control: Full
Dynamic Racing Line: Always on
Racing Line Type: 3D
Gearbox: Automatic
Pit Assist: On

General:
Don't forget to use your KERS coming out of turns and the DRS when available (pretty much only during qualifying).
You can't run rich fuel the whole race, and be careful running it at the start as it will overheat your engine very quickly coming from a full stop, but it can help in those situations where you qualified a little further back and need to get in the lead. Once you get there, remember to turn it off, so you don't find everyone passing you as your car dies on the last stretch.
Your qualifying position does not matter a whole lot on most races. You will be able to get to 1st from last place within the 1st lap usually. Malaysia was one of the toughest for me, I would definitely try to qualify in the top 10. Monaco is also a little tricky because there aren't a whole lot of great passing areas, but there are at least 2 chicanes (zig-zags basically) where you can pick up a lot of ground.
I've included pictures of each track which number the turns. I've rotated them to match the on screen map (when you have it in non-rotatin mode). I've also color coded each turn as to how fast you can go through it. Green you can go pretty much full tilt, yellow slow down a little bit, red come to almost a stop (definitely under 100mph in most cases). These speeds assume you are using the shortcuts below, there are plenty of turns you obviously can't do at full speed unless you are cutting across the grass in a major way.
I've also provided a description of many of the turns, mostly where you can take a shortcut.


#1 Australia
Some great cuts, pole position should be relatively easy.
1/2 cut straight across, let off gas as you go over 2 a bit so you dont hit right wall
3/4 slow down quite a bit feel free to cut the corner as well as the following one
6 slow down a bit for this one
9/10 cut across both about where the side road is
11/12 cut acoss but not too far to the right or you'll hit sand
13 slow down quite a bit feel free to cut the corner
14 you should be ok just letting off gas on this one
15 will need to slow a little and there is a lot you can cut
16 don't forget to burn your DRS/KERS


#2 Malaysia
No good opportunities to cut here so it may be difficult to qualify well. I managed to win from 13th, but it took several restarts to succesfully thread my way through the pack at the 1st turn and come out in the lead. Not too hard to hold 1st once you have it, but I had a hard time catching up if anyone got more than a very short distance ahead of me. There is a lot of sand on this track, punishing you for straying off the track.
Don't despair on this one. If it is driving you nuts, you can skip it, or be satisfied with a low placement. If you have 2 drivers, I would definitely not waste too much time trying for the win on this, you can easily make up the points later.
1/2 cut across these, you can pick up some positions in 1st lap, not so great after that
4 cut this a bit but not the grassy part (or if you do, slow WAY down) as a bump at the end will send you into the air
6 just ease off the gas a moment then reapply
7/8 slow down a bit for 7 and you can take 8 at almost full acceleration
9 slow down a lot, you can cut this one a tiny bit
11 i found this awkward to cut, just slow down a bit
14 same as 11, burn some KERS coming out
15 you can cut this a little bit


#3 China
1/2 you can start this out fairly fast but will need to brake gradually as you go around
3/4 you can cut this one a bit
5/6 if you bear right on the paved section at 5 you can do a huge cut here
9/10 you can cut a bit off of 9
11/12 you can cut across both of these pretty well
14 you have to slow down a bunch anyway and there's a fair amount you can cut here
16 small possible


#4 Bahrain
1/2 cut this as soon as you can and you will skip right over 2 entirely, you don't even have to brake
4 minor cut here
5/6/7 cut 5 far to the right, you will slow down a little but come straight into 6
8 you can cut here, the sand will slow you down quickly
9/10 cut but slow way down for 10
11 cut here
13 cut here but don't go wide or you'll end up in the sand
14 You can cut a little off here


#5 Spain
1/2 cut across straight into 2
5 cut here but careful of the sand
7 cut across here but you will need to avoid sand on the left and then on the right as you go into 8
10/11 cut a bit off 10 and 11 at the same time
13 cut a little off here
14/15 plow straight through both


#6 Monaco
I would definitely turn off damage on this one
1 you could cut a tiny bit here
10/11 first real cut, just go straight
15/16 go straight across


#7 Canada
1/2 cut straight across both but slow down to get back on road
4 easier to cut this a bit coming out of 3
6/7 cut both but not too much on 7 or turn is too sharp
8/9 cut across 8 straight into 9
10 can cut a lot but still need to low way down
12/13 you can cut these a little but if you go too far it will magically cut your speed or send you spinning


#8 England
(On the map I have the starting location is different, so the race starts right before 12)
14/15/16 Cross over most of 14, aiming just to the right of the yellow cap on the wall at 15. The sand will slow you down quite nicely.
17/18 You will need to slow down on 17 and even more for 18, but can still make some big cuts here
4/5/6 Don't turn at 4, just plow straight across at full speed and into 6
7 you can cut some here if you want but not really needed
9/10/11 skip 9 and aim just left of the wall at 10, the sand will slow you, then get back on track


#9 Germany
1 you can cut a bit here but need to slow way down regardless
2 cut a bit here but get back on road quickly
5/6 cut this curve as soon as you can and aim a bit to the left of the french flag. as soon as you clear the gravel, turn hard right, you shouldn't need to brake.
7 slow way down, cut from far enough to the left that you don't go into sand on the other side
11 not worth cutting, just slow down a tiny bit
13/14 safest thing is to cut left early over a tiny gravel strip. it will slow you down enough that you dont become seriously airborne


#10 Hungary
1 you can cut a little here
3 cut a little here
4 and a bit here
6/7 only serious shortcut on the track, bear a bit right at 6 and you can skip both
11 cut a little here
12 moderate cut here


#11 Belgium
7/8/9 A little tricky, but com from the left edge of the road and cut the 1st corner, get enough to the right to clear the wall at 8, and brake hard when you are back on the road.
14 you can chop off a little here
19/20 another tricky one you want to gon onto the grass right after the 2nd rolex sign. you want to aim roughly in between the red roof on your left and a truck with a TV on top on your right. as soon as you get back to pavement brake and turn left


#12 Italy
1/2 You can fly through here at full speed just aim a little bit right
4/5 You can fly through here at full speed just aim a little bit left
8/9/10 Best way is to cut left as much as you can through 8, avoiding the sand to your right at 9, then immediately bear right to avoid the sand on the left at 10.


#13 Singapore
I would definitely turn off damage on this one. I got the driver's championship after this one. (325 points, Massa was 2nd at 140). This could come a little sooner or later depending on how much you have been interfering with the top drivers. For reference at this point in the season construtcor's challenge was at 325 and ferrari in 2nd at 220.
Unless you have 2 people it will likely take a bit longer for the constructor's cup, as you need a 43 pt margin for each remaining race. For driver's you only need 25, so at this point, a 150pt lead is enough. You would need 258 to clinch constructor's here. (Totally doable with 2, as i would have been up by 334 at this point if we had been getting consistent 1/2 finishes (and that's not even counting that the other teams would have missed out on thos points as well).
1/2/3 take 1 tight, cut across 2 and slow down immediately to cut 3 as well
5 slow down a bit and cut a little off the corner here
7 you can cut a little here so brake and turn a little early
9 you can cut a little here so brake and turn a little early
10 you can cut a little here so brake and turn a little early
11/12 you can go pretty straight through here
13 very sharp you need to start braking around the 50m sign
14 you can cut a little here so brake and turn a little early
16/17 like 11/12 but not quite as good
18/19 brake around the 50m mark, you can cut a bit on 19
20/21 like 11/12 but not quite as good
22 you can cut a little here
23 don't take this last turn too sharp or you'll pit


#14 Korea
1 you can cut off a nice amount here
3 you can cut off a nice amount here
4/5/6 you can cut straight across here, they will cut your speed way down but it is still worth it if only because you can't mess up as easily
9/10 turn just a bit at 9 and you can skip 10
12 easiest to just cut this coming out of 11
14/15/16 you can do little cuts on all of these


#15 Japan
3 You can cut this a bit here
9 decent cut opportunity here
11 don't try to cut this too much or it will reset your car
13/14 i would cut here as soon as you clear the sand, keep enough to the right of the wall at 14 that you have room to turn and start braking and turning a little before the grass
15 just let off on the gas a moment here
16/17/18 cut right as soon as the wall ends and aim for the edge of the bleachers to the left of the ferris wheel


#16 India
I had the constructor's championship clinched at this point. 400 to 257 (infiniti).
1 You can cut here and be lined up nicely for 2
3 You can cut this but have to go pretty slow so you don't go flying off at the end. definitely use some KERS coming out of this one.
4 There is a narrow side track you can take that shaves a fair amount of distance and is a much gentler curve, it is rather narrow though.
5/6/7 don't take 5 TOO fast, as if you turn a little more sharply than normal you can skip straight into 7.
8/9 Cut 8 rather than 9, as 9 has a sand trap
10 There is an inner track here, but i would skip it, as you can take this curve pretty fast since it's banked
12/13/14 I cut straight across at 12 and skipped 13
16 you can cut a bit here, but still need to slow down as you don't want to go too wide and end up in the pit


#17 Abu Dhabi
5/6/7 shoot straight through, you'll still need to slow for 7, but not as much (brake hard about 1/3 through shortcut)
8/9/10 you can nip off a bit on 8 and skip 9 entirely
11/12/13 cut across 11 if you want but 12 you can skip straight over
14 chop off a bit here, turn before the side road and you needn't even brake
18 you can cut this one a fair amount
21 careful not to cut this, it will reset your car


#18 Austin
1 you can cut a lot off this corner
3-9 its best to do this mostly legit. you can go pretty fast through these. if you want to cut just do a bit off each tip, dont try to cut straight across
11 you can cut a bit off this sharp turn but still need to slow down a lot
13/14 slow a bit and cut across be ready for another cut left
15/16 the sand should slow you enough that you needn't brake
19 hit this at speed and cut the corner a bit
20 definitely cut this but not too much (or you'll pit) or too fast


#19 Brazil
Hopefully you have your trophies by now. If not, last chance!
2 you can cut right through here
4 you can cut a little here
8/9 cut across 8 then straight through 9, just right of the crane
10 cut this as much as you can (given the wall)
12 cut this at about the 50m sign and you will only have to brake a little bit