This requires about 10,000 adam, which amounts to 3 hours of playtime and 25 games, give or take, to unlock. If you're good enough to get plenty of killstreaks, this'll go even faster. Some tips;
1) Hack and research everything you can. +10 per hack adds up fast, and it'll help you get kills.
2) At the beginning of each match, look around for adam vials. A lot of players skip these, but it's an easy way to gain +50 each match.
3) Dont quit out. Your progress will not be saved, and you'll lose out on the game completion bonus, which is 100 to 200 adam.
4) Pick up the big daddy suit whenever you can. It's an automatic +50, and you're almost guaranteed a killstreak, for another +50, on top of all the easy kills you get. If you're fighting a big daddy at full or near-full health, hit him once and run. You'll be counted for an assist. If you think you could kill him, go earn that 100 adam, but beware of killstealers.
5) Completing the trials for Incinerate, freeze, and shock is well worthwhile. So are the ones for your favourite gun. Areo dash and whirlpool are less important (becuase they're harder and slower, you can earn adam faster). For the most part ignore the rest until you reach a higher rank.
You can also boost this, for a good guide on boosting, see JxOxHxNxSxOxN's solution here;Solution for Choose the Impossible in BioShock 2 (PC)
If you have any questions, further advice for this game, or ways to improve this solution, please post a comment.