Once you are in Dead Ops Arcade, during the first mission, you can round up all the zombies without killing any. Lead them around the small island until they get packed in together and then use the speed boost to blast through them. If you were able to get 20 in one hit, the achievement/trophy will immediately pop. If you missed getting the full 20, just restart the level and try again.
Just like the “Insert Coin” achievement/trophy, but instead of typing in DOA, you will need to type in ZORK. Once you do, the classic text game will load up and you’ll get the goods for minimum effort.
For this one, you will need to kill 5 enemies with one grenade. The easiest way to do this is to get a group of enemies that are gathered around a vehicle and toss the grenade at it. The resulting blast will be much larger and more devastating than just a grenade explosion.
Play some Wager Matches in Multiplayer and be in the money for 5 rounds. Pretty self-explanatory really.
Complete the second mission, Vorkuta, to obtain this.
When you reach level 3 of the Pentagon Nazi Zombie map, Five, and the power has been turned on, there will be an announcement saying “Breach Detected on Level Three.” The Thief- who is dressed like a scientist- will appear randomly and start to chase after a player. This is easiest to get when you have a group of four, since the other players can fire on him while he is chasing down one player. The thief will chase each player one at a time until he steals your weapons. Have everyone take him down as fast as possible and when he goes down, you can recoup your guns as well as some other nifty treats to help with the other Nazi Zombie achievement/trophies.
Near the end of the Victor Charlie mission, you will enter a village and need to clear it out. When you do, up next will be a gun emplacement on the river to the right. Use the Grim Reaper launcher to destroy it. Keep the launcher with you and continue through the village until you come to a machine gun nest that becomes uncovered. Use the launcher to take it out and move along.