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The 5 Flashback maps you need to play on are:
It is possible to gain this achievement solo in local multiplayer. Simply set up a local multiplayer match (do not select Wingman) against 1 bot. Warzone is probably the fastest when setting it to be a 1 kill win.
After selecting the correct map pick your character and weapon and start the match.
Hunt down your oponent and kill him to win the match.
Once you win the game just set up another match but on the next map :)
After winning the match on the final Flashback map you will gain the achievement.