Here is the full list of all 18 Pursuit of Redemption achievements.
Finish Level 1.
Find your first collectible.
Find collectible #2.
run out of fuel, jump off the desk with your parachute, and refill your jetpack in level 2.
Complete all Time Objectives.
Complete all heart objectives.
Don’t lose a single heart throughout the entire game.
Complete all Objectives.
Don’t use shield in any of the jetpack levels.
Find all Collectibles.
Complete Jetpack 1.
Complete Jetpack 1 and 2, without dying a single time.
Pass the River of Death in Jetpack 3.
Complete all Jetpack levels.
Complete the maze level without dying.
Turn all the Valves in the maze level.
Don’t skip any of the cutscenes (Including Credits!)
Unlock all trophies of Pursuit of Redemption.