This is an easy trophy which will come in time as I'm sure nobody in their right mind will play this without taking up everything it has to offer but nevertheless...
You have to play ONCE on every multiplayer mode which are:
Fighter Squadron - An all out aerial deathmatch
Supremacy - Capture and hold points on the map whilst stopping the opposition from doing the same.
Cargo - Capture the cargo and return it to your base whilst stopping the opposition from returning theirs.
Droid Run: Play as a team of six to capture three GNK Power Droids and hold onto them whilst stopping the opposition.
Walker Assault: An epic 40 player battle between the rebels and imperials using walkers & Y-wing bombers.
Blast: A classic team deathmatch for up to 20 players.
Drop Zone: Find the drop pods as they crash down from orbit, hold onto them and stop the opposition from taking control. Highest number of drop pods claimed at the end of the match wins.
Heroes Vs Villains: Take turns playing as classic Star Wars heroes and Villains and destroy the opposition. A 12 player match.
Hero Hunt: Hunt down the hero and destroy him before anyone else does... then become the hero yourself and get as many kills as you can. The most kills AS a hero at the end of the battle is the winner.
Simply take part, win loose or draw in all of these online modes and the trophy is yours! My advice would be to keep going at a mode until you've won at LEAST once and then you'll also get the "In a galaxy far, far away trophy too" (WIN once in every online multiplayer mode).
Do this methodically, work your way through the list so you know where you've taken part and or won. If you can't remember, go to your stats and it will tell you how many times you've won each game mode.
Good luck!