While I have not yet(as of 1/11/13) unlocked this trophy, I am pretty close so I thought I'd share some tips in case you can't/don't want to boost.
As soon as the match starts, scrounge around for the red adam vials, they give you 10 adam a piece and are super easy to pick up
Until you get a better selection of plasmids and weapons; the shotgun and dash combo is really effective.
At least here in the UK, most of the game modes apart from Civil War are pretty quiet, but you pretty much always find a game in Civil War so stick to that.
Research every one you kill, not only does it double the adam you get(10 for the kill and 10 for the research) it gives you a damage increase against that foe until they kill you or the match ends.
Hack everything, this means turrets and vending machines, not only do you get 10 adam per hack they also rack up a good amount of kills for you.
I dont think I need to say get the Big Daddy suit whenever possible but when you do, put your bombs in front of door ways for best effect but keep a couple behind incase the enemy tries to swarm you.
When a foe gets the Big Daddy suit don't try to be a hero, it's not worth the time or deaths to try and take them down by yourself and, chances are, your team will swarm them anyway. When the Daddy is close to death, swoop in for the kill for an easy 100 adam(scumbag tactics ftw)
Activally be trying to complete at least 1 trial at all times. The rewards for completing them range from 75 to over 500 a peice, with dozens in the game they will give you a good number of levels by themselves and save you a lot of time, as well as giving the proceedings some much needed variety.
A most people online use a combo of electricity and either the elephant gun or crossbow to stun lock you and get a one hit kill headshot. Have a class that combats this well in reserve, I use bees and a shotgun to take their precise aim away and allow myself time to close in for the kill. If you encounter a game where this is going on a lot, switch to such a class to counter it.
Hope these help, and good luck!