Here is the full list of all 12 Flashback achievements.
Complete level 1 (Jungle)
Kill an enemy indirectly
Complete level 2 (New Whasington)
Complete level 3 (Death Tower)
Complete level 4 (Earth)
Complete the game on Easy
Complete the game on Normal
Complete the game on Expert
Without using Rewind on easy/normal
Without using Rewind on Expert
Kill 50 enemies
Kill 200 enemies