Here is the full list of all 56 Bad Pad achievements.
Finish area 1
Win your first arcade mini-game
Defeat Evil Pen again
Get Drop Bash upgrade
Collect 20 coins
Finish area 1.3
Finish the second carting level
Finish area 1.2
Get glow in dark upgrade
Win your first battle against Evil Pen
Finish the first carting level
Meet Analog, he will help you!
Open and go through your first door
Collect your first coin
Blow up your first rock
Find and talk to TrapeZoid
Think you're a good runner, try Bad Run!
Collect 50 coins
Collect all coins
Solve crates puzzle
Finish area 2.1
Get through the first submarine level
Meet LT and RT and get some help
Defeat Evil Pen Water Monster
Finish area 2.2
Finish Area 2.3
Shrink down
Get through the second submarine level
Take down Evil's Pen Submarine
Finish Area 2
Win the second arcade mini-game
Finish Area 3.1
Finish the crate puzzle
Finish Area 3.2
Falling is fun, diving is more fun, get the Air Diving Ability
Finish the third carting level
Get rid of the spider
Finish Area 3.3
Square, Big, Strong, arggghhh.
Get through the maze
Take down Evil Pen's Train
Finish Area 3
Finish the forth carting level
Finish the fifth carting level
Win the third arcade mini-game
Finish a game world scene
Finish Area 4.1
Finish a water pipes puzzle
Finish Area 4.2
Finish Area 4.3
Finish Area 4.4
Win the last stand off
Finish the game in easy mode
Finish the game in normal mode
Finish the game in hard mode
Pick up all collectables