To unlock his achievement you need to simply play a match of every game type (Winning the match is not required). Here is the list of the nine different game types:
Supremacy - 20 vs 20 Tug of war point captures game
Walker Assault - 20 vs 20 AT-AT attack & defend game
Fighter Squadron - 20 vs 20 Team death match with Starfighter dog fights
Blast - 10 vs 10 Land based team death matches
Cargo - 6 vs 6 Capture the flag game type
Drop Zone - 8 vs 8 Claim and defend drop pods
Droid Run - 6 vs 6 Claim and defend mobile droids
Hero Hunt - 7 vs 1 Hero vs enemy squads
Heroes Vs Villains - 6 vs 6 All heroes team death match