Defiance Free to Play

You DO NOT need to reach 1000 rep with 7th Legion.

*Confirmed: This unlocks with the "7th Legion Shogun II" Pursuit. *

This pursuit requires:

-Complete 25 daily contracts for the 7th Legion = At least 25 days

-Complete 5 weekly contracts for the 7th Legion = At least 3 weeks.

-Reach Reliable status with the 7th Legion = 300 7th Legion Rep

-Buy 10 items from 7th Legion vendors = At least 500 7th Legion rep and 80k scrip.

The daily and weekly contracts should be your main focus. The more consistent you can be in completing them the more you'll gain rep naturally.

25 daily incursions = 250 rep alone.
The daily has so far always been to complete any incursion during the day for 10 rep.

Individual incursions get you 5 rep, so from the 25 daily you get an additional 125 rep.
(There is also a clan rep bonus that can apply which will give you more rep in the long run.)

So from just doing the daily incursions you get 375 rep, comfortably covering your "Reach Reliable status" portion of the pursuit as well.

There are two weekly contracts available every week for 7th legion. One for 15 rep and another for 35. If you complete both of these in two weeks and the 35 one on your third week you will finish off the 5 weekly contract portion of the pursuit as well as gaining an extra 135 rep putting your bare minimum rep at 510.

Then spend your 500 rep and 80k scrip buying 10 Mod caches from the 7th legion vendor at Overpass.

The Mod Cache is the cheapest item from 7th legion. They cost 50 rep and 8k Scrip, thus the above total required.

Good luck grinding. The soonest you can get this is 25 days from the start.

--I will leave solution alone other than bold out an extra sentence no one has seamed to have read, and have marked me down. The guide was complimentary to the first solution and cover all bases, BEYOND the achievement, and well as detailing the achievement.
It was originally undetermined what was the unlocking condition, so i wrote a guide for all conditions. But the Answer section was always correct, and details what you need for the achievement, then what you need IF you want the 1000rep for the following BOLD questions..--

As an complimentary add-on for the above post,
i thought id add an estimation for those wanting an answer to:

- Quickest way to 1000 Reputation with 7th Legion?

- If i played 1 Incursion per day, would that be enough?

- What is the most economical way to Max the 7th Legion Reputation?

- Cheapest way to buy 10 items for the pursuit?

- How do i get "7th Legion Samurai" Title

------------------ANSWER---------------
Complete 25 daily contracts. 1 Incursion per day.

If you are just after the pursuits / achievement, you will not need to do additional Incursions.

If you want 1000 Rep for weapons or the "7th Legion Samurai" title during the 25 days, then during this time you will need to complete an ADDITIONAL 82 Incursions.

This could be done by completing 4-5 Incursions per day, over 26 days without wasting time, as you will also net your weekly contracts also, if you find all 5 the different locations (Incursion Crusher), and also complete the 3 required Arkfall bosses (Triple Threat Weekly Contract).

Then just buy 10 weapons from the 7th Legion Vendor in San Francisco, Overpass.
Cheapest is the Mods for 50rep, 50x10=500rep.

Explanation and TIPS below

------------------NOTE--------------------
-You need to hunt down the new INCURSIONS.
They will appear as a Yellow Radiation symbol, in the world and on your map, press BACK to open the Map and search around, using the thumb stick.

-To see Contracts for progress for the achievement, Press START, HOLD left trigger to see wheel, Go to top right for Contracts and Pursuits, Tab to contracts with RB shoulder button.
Look at the Reputation for 7th Legion.
-Pursuits are at the bottom of the previous page, and conditions outline above, in previous post.

---------------- Time saving TIPS --------------
If you are having trouble knocking out 5 Incursions per day in a reasonable time frame, Trion have now made it so 2 Incursions are normally on at the same time.

You could also hop Phases/servers/shards to look for more Incursions by doing the following:

-Contract reset at
7pm GMT (UK)
3pm EST
Noon PST

-Have friends you can switch to.
Hit RIGHT on Dpad > Friends > Join Friend.
This will put you in the same phase as them.
Hit BACK button to look at your map, and take a look to see if there are any Incursions on.

-Switch to a Shadow War and exit
This will generally place you in a new phase.
When you exit you can use the Map again to look for more Incursions.

-Ask in Clan chat, and Group up
Hit LEFT on Dpad and switch to clan chat, hopefully some one will answer.
Then either use the above method, ad go to Clan rather than Friends to group up.
OR go to the SOCIAL page on your wheel, hit RB to go Clan.
Select a member off the list to Group up.
If you are the leader, promote them to leader, then you can hop to them. Hit Right on Dpad > Group > Join Leader.

Buying 10 weapons
These do not have to be full weapons.
You can just buy 10 mods. One of the mods available is 50rep.
50x10=500rep, so you will have enough just by doing the 25 incursions and weeklys.

------------------EXPLANATION---------------

Longest time constraint is the DAILY contracts completed = 25.

28 Days are in 4 weeks so this will take 3.5 weeks, if you do each Daily contract.

This would ALSO net you the Weekly contracts, as you will get 2 per week = 6 /5 Weekly contracts

If played it smart, and each of your Daily contract Incursions were in a different area/location each time, and got all five Incursion locations within the week, this would give you the contract for the week too (Incursion Crusher).

Of course though, if you only played one Incursion per day for 25 days, your 4th week would end on 4 incursions completed.
So playing an extra day (26) would net you your 6 weekly contracts completed, if you are also completing the ArcFall bosses, listed in the contracts (Triple Threat Weekly Contract).

If you are in a good clan, and are getting the additional 5% rep bonus!!

Unfortunately this will only give you 1 Rep per week.
- As i am aware, this must be given to the Contract for 35 Rep points.
35 Rep x 0.05 = 1.75 = 1
15 Rep x 0.05 = 0.75 = 0
5 Rep x 0.05 = 0.25 = 0
Rounded down to solid number. FAIL :(
---
Daily Contract give 10 Rep
10 Rep x 26 Daily's = 260 Rep

Incursions give 5 Rep
5 Rep x 25 Incursions = 130 Rep

Weekly Contracts give 15+35=50 Rep
50 Rep x 4 Weekly's = 200 Rep

Weekly Clan boost of 5% on 35 Rep
35 x 0.05 = 1 x 4 Weekly 35s = 4 Rep

290 + 130 + 200 + 4 = 594 Rep From doing 1 Incursion per day.

------------------CONCLUSIONS---------------
*Everyone seems unsure what the trigger for the achievement will be, if it pursuits + Rep @ Reliable, OR if it will be higher.
So here is a list of no of additional Incursions you may need.

7th Legion - Reliable - 301 Rep = *If the achievement is for completing the 7th Legion pursuit, you would be done after hitting your 25 Daily Incursions.

7th Legion - Reliable Complete - Trusted - 601 Rep - 594 Rep = 6 Rep
= 2 Incursions NEEDED
If only 600 Rep for Familiar is needed, then you only need to play 2 additional incursions

7th Legion MAXED - 1000 Rep - 577 Rep = 406 Rep NEEDED
423 Rep / 5 Rep from a single Incursion
= 82 Incursions still NEEDED
If though you need/want 1000 Rep to max out the Reputation for the 7th Legion Faction, you will need to have played an ADDITIONAL 82 Incursions to max it out over your 26 days.

82 + 26 = 108 Incursions / 26 Days = 4-5 Incursions per DAY

Then just Buy 10 Weapons or Items from the
7th Legion Vendor in San Francisco, Overpass
-You can buy Mod boxes for 50 Rep x 10 = 500 Rep
So you will have enough to finish the pursuit either way :)
- Do this AFTER you have reached filling the Reputation for 7th Legion, just encase it eats at your reputation grade.

---------------------------------------------------------

Hope that helps!

Sorry if looks overly complicated, but all the information you need for a fluid economical experience without you shooting yourself, is outlined at the top in the answer.

4-5 Incursions over 26 days should net you 1000 Rep and the achievement, if not before.

It will allow you to buy any weapon or item from the 7th Legion vendor, as well as the tittle "7th Legion Samurai"

If you have any criticism or additional data to support errors,
PLEASE COMMENT, rather than just hitting thumbs down.
Ill be the first to admit if I have made a mistake.