GRID 2

Addition:

You have to choose "Race" to get this achievement.
Other game-modes like "Touge" will not work.

So. Set up a private match with your friend, choose "Race" and a map that lasts only 1 round.

Cheevo will pop immediately after both are behind the finish-line.

This achievement can be easily boosted for those that aren't too great online.
Once you have fully upgraded a car just set up a race, for the relevant tier group, in 'create online event' and take it in turns to win.

This is the best way to get the achievement as you can make the race private, meaning no randoms can join.

You must own a car before you can upgrade it.
You can unlock a car by entering a Global Challenge, ie I unlocked an Aston Martin Vanquish in tier 3 today by entering the first available listed global challenge but you wont be able to upgrade a high tier car without leveling up considerably so you will either find it easier to use a car from the VIP pass for example the tier 1 Alfa or you can participate in global challenges and multiplayer playlists to earn in game currency and purchase a car to upgrade. You will also need some money from either partaking in challenges or multiplayer events to buy an upgrade

Apply at least one upgrade to any car in any tier, it does not have to be a fully upgraded car.

Select your upgraded car for the next available race of the cars tier and win.
It must be a race and any race in a series of events will count as long as you selected a car with at least one upgrade.

This can be obtained in standard playlists that include race events or any other public or easiest to boost private match up as long as it is a race, you win using an upgraded car.

Easiest legit method is take a tier one car and upgrade it to top out tier one, start a public lobby with desired number of short race events and wait for someone to join you which should not take long and will most commonly be a low level player. Start the event series and win one of the races.

Otherwise boost it in a private lobby with a boosting friend.

Hi, guys.
To get achievement Harder, Better, Faster, Stronger, you need upgrade one of your cars to full and with that car win one race. Select event with required Tier , select your upgraded car, that is on needed Tier and good luck to win.
I get achievement online, when fully upgrade Alfa Romeo to Tier2 and win random race.

4 years on from these solutions - the game is mostly played by LVL99 fanatics. To make it worse they put collisions On and shunt you off the track to cheat - as though their car wasn't twice as fast anyway . Selecting a Race playlist is unlikely to get you the victory in the tier/car you upgraded.

Best/quickest way now:
1. Get Social Butterfly first and use the earned money to upgrade the Dodge Challenger SRT8's top speed (drivetrain), keeping it in tier 2.
2. Select ONLINE CUSTOM EVENT > CREATE GAME.
3. Set the event to: RACE; TIER 2; 5 ROUNDS (doesn't give Social Butterfly, but might lure in people hunting it); VERY EASY (AI cars, as a distraction). Advanced options: I was on pole using XP LEVEL* (I was LVL4); COLLISIONS OFF; FORCE MANUAL GEARS ON (This may catch out total noobs); IMPACT RATINGS ENABLED (Avoids shunter scum players?).
4. TRACK SELECTION: Select the 5 shortest tracks you know - I knew Brands Hatch Indy/Rev well, so learn that and set it to 2 laps (just in case you're not on pole).
5. Hit DONE and wait for your event lobby to have some low level noob/s join and quickly START the first race (I had 3 LVL1s join*! In June 2017).
6. Win the race in your upgraded SRT, easily.

* If you find that higher level players are joining and they're on pole position then try setting the grid to XP LEVEL REVERSE.