Here is the full list of all 33 Wolf and Pigs achievements.
Complete every 'Kill the Pig Soldier' side mission in Stage 1,3
Complete every 'Open the Treasure Chest' side mission in Stage 1,2
Complete every 'Clear in Time' side mission in Stage 2,3,4,5,6
Complete every 'Rescue the animal friends' side mission in Stage 4
Complete every 'Clear with 50% or more HP' side mission in Stage 5,6
Stage 1 "Easy Warm Up" Clear
Stage 2 "Chase Like Walk" Clear
Stage 3 "Illegal Construction Site" Clear
Stage 4. "Entry into an Arena" Clear
Stage 5 "Garbage Dump" Clear
Stage 6 "Public Execution" Clear
Ate Rotten food x30
Ate Recovery food x50
Picked up a bone or can x30
Clear Stage 1 with S Rank in 1 minute
Clear Stage 2 with S Rank in 55 second
Clear Stage 3 with S Rank in 1m 50s
Clear Stage 4 with S Rank in 3 minute
Clear Stage 5 with S Rank in 1m 40s
Clear Stage 6 with S Rank in 3m 20s
Acquired a machine gun
Acquired a shotgun
Acquired a charge gun
Get rid of 100 pig soldiers
Game Over
Fall 10 times
Clear every achievement
Clear Stage 1 with S Rank in 1 minute - Hard
Clear Stage 2 with S Rank in 55 second - Hard
Clear Stage 3 with S Rank in 3m 40s - Hard
Clear Stage 4 with S Rank in 5 minute - Hard
Clear Stage 5 with S Rank in 2 minute - Hard
Clear Stage 6 with S Rank in 5m 20s - Hard