Just copied a list of some of the trophies from the game. Though you can't get all of the single player trophies in multiplayer, it is possible to get all of the multiplayer trophies playing single player. I thought this was a pretty smart way to satisfy both types of players.
Start a character in multiplayer or customize a character in single-player.
Tour of Duty (Bronze)
Finish all multiplayer maps or all N7 missions in single-player.
Complete one multiplayer match or two N7 missions.
Complete three multiplayer matches or five N7 missions.
Almost There (Bronze)
Reach level 15 in multiplayer or level 50 in single-player.
Peak Condition (Bronze)
Reach level 20 in multiplayer or level 60 in single-player.
Promote a multiplayer character to the Galaxy at War or import an ME3 character.
Finish all multiplayer maps on Gold or all single-player missions on Insanity.