Romeo Alpha DeltaG 15

This will likely be the only achievement in the game that will truly challenge you and not just rely on grinding coins or getting lucky. The gravity belt is a recommended tool since it gives you better precision control over Barry, and the other gadget is up to you. I went with the insta-ball just because I knew I'd lose my mind if I had reached 4,930 or something like that and just needed those few extra meters, but it's totally your call based on your play style and what you think will help the most.

Get as many spin tokens as you can, since there's always a chance these will give you a bit of help with second chances and small/big/atomic blasts. Don't take stupid risks to get them, obviously, but if it's between coins and a token, go for the token. Also make sure to pick up vehicle tokens whenever possible, since even the crappy ones (looking at you, Gravity Suit) will give you the ability to take a hit and keep on running.

This was all I personally needed to unlock the achievement, but you also have the option to purchase a final blast and a quick revive, which you could activate to give you the option to rack up some more distance, though it's recommended you not waste the coins on these unless you're sure they'll be the difference you need (3500m+ for a quick revive, 4800m+ for a final blast). Again, this will be a challenge, but not an impossible challenge by any means.