There's no guarantee to get this achievement. But here's a fairly detailed guide to help you with it, including some insider tips from the devs. (There's also a TL;DR summary below.)
I'd strongly suggest playing the game once or twice before reading the guide, otherwise it'll just be confusing.
Getting to the final showdown:
This is the easy part. Stay near the outside of the arena, just inside the circle and let other players battle in the middle of the map. Drive around near the edge and grab car upgrades when you can. Off-road cars are usually your best bet.
Watch your mini-map. If someone comes towards you, try to avoid them! But note that head-to-heads usually finish towards the center of the arena from where you are. Always be aware and ready to race if you do get challenged. Start racing immediately - don't wait until the destination pops up. If you face the right direction you'll almost always get a nice head-start on your opponent. (There are exceptions sometimes. But it's still your best bet - especially in slow cars!) With this strategy I make it to the final showdown more than half the time.
PS: You can supposedly "hide" from other players by stopping your car and you won't show up on the map. In my experience this doesn't work reliably - people seem to find me no matter what.
Starts when there are 12 players left in a reasonably full game (max. 72 players.) Or about 6 left in 36 player games. (May vary. But this is my experience.)
With about 20 players left (or 10 in smaller games,) check the map to see where the final ring will be. The finish is usually towards the center of the map from where the ring is! (There are rare exceptions. If the final ring is near Edinburgh, the finish often seems to be in the city, for example.) Once the final ring is indicated by the outline on the map, slowly make your way to a road which leads to your expected finish, still avoiding other players. (If the final ring happens to be exactly in the middle of the map, you'll just have to guess a direction. Go where no one else is and hope for a bit of luck!)
When the countdown starts, get close to the edge of the arena (facing your expected finish.) You want to accelerate and time it so that you break through the barrier about 3-4 seconds before the countdown ends. You can survive outside the ring for 5 seconds, so take advantage of it. When the final destination pops up, adjust your course and go!
PS: If you're challenged in the final ring, remember that head-to-heads are cancelled when the countdown starts! It's a valid strategy to ignore the challenge and hope that someone else gets eliminated before you, since a head-to-head at this point leaves you out of position with little chance of winning the game.
If you guessed the right direction you'll have a good chance. Keep in mind that supercars don't handle well off-road. Stick to the streets if you can. In off-road cars, anything goes.
Check the map occasionally on a straight road or field (take your finger off RT to stop zooming in) and keep an eye on the best route, avoiding lakes, etc. Try not to hit any obstacles, slow down if you need to, beware of walls around towns (!), and you'll get that win eventually.
Obviously other people may also guess the right direction. But I've been in final showdowns where literally no one else was even near me. They all tend to cluster together. With a little luck they're all on the other side of the arena and you get a nice head-start!
See where everyone else is lining up and go in the opposite direction, hoping you get lucky. :-)
- Pick up better cars; Avoid challenges
- Races usually finish towards the middle of the map
- You can leave the final arena 5 seconds before the countdown ends
Other notes and tips:
Don't play Eliminator when you're frustrated. It's battle royale, so people will try to eliminate you. Don't get upset about it. Everyone wants to win and no one knows (or cares) about your achievement hunting. Get in the right frame of mind before starting. A full game will take about 20 minutes.
This strategy is NOT for the "Heads Up" achievement (winning without car drops) and hence not for the completionists among you. But you could of course combine certain aspects of it.
Lastly, if there's anything I can do to improve the guide, let me know in the comments. Please don't downvote just because you didn't win first time. This is simply a guide which has worked really well for me. It's not a guarantee. (There isn't one!) It may still take you quite a few attempts to win a game.