Full list of all 27 Bad Piggies achievements worth 235 gamerscore. It takes around 8-10 hours to unlock all of the achievements in the base game.
The base game contains 20 achievements worth 200 Gamerscore, and there is 1 DLC pack containing 7 achievements worth 35 Gamerscore.
Checked the credits
Episode 1 completed with 3 stars on all levels
Gained 3 stars in all blue levels in episode 1
Episode 1 completed
Finished 50 levels without breaking anything
Traveled 1000 miles in a transport
Complete Episode 3
Complete episode 3 with 3 stars on all levels
Gain 3 stars from all blue levels in episode 3
Break off 1000 parts
Transport King Pig successfully 50 times
Start a transport with 25 or more parts
Pop 100 balloons
Discover 20 explorer remains
Use a Turbo Charge power-up
Use a Super Glue power-up
Use a Super Mechanic
Use a Super Magnet to collect all cakes and a starbox in 1 run
Complete Episode 5
Complete Episode 5 with 3 stars on all levels
Break a bridge.
Drop into a certain pit in Little Pig Adventure sandbox.
Collect the star in the labyrinth in Little Pig Adventure sandbox.
Collect all the stars from Little Pig Adventure.
Collect a star with chain reaction in Little Pig Adventure sandbox.
Collect the Alley-oop star in Little Pig Adventure sandbox.
Use the gearbox in a contraption.