Here is the full list of all 19 Invercity achievements.
Clear World 5
Clear all puzzles in World 5
Clear all puzzles
Collect all remote controls
Clear the game
Clear all puzzles in World 4
Collect all remote controls in World 4
Clear World 4
Clear all puzzles in World 3
Collect all remote controls in World 3
Clear World 3
Clear all puzzles in World 2
Collect all remote controls in World 2
Clear World 2
Clear all puzzles in World 1
Collect all remote controls in World 1
Clear World 1
Clear Stage 1-3
Clear Stage 1-0