Here is the full list of all 10 Woody Two-Legs: Attack of the Zombie Pirates achievements.
Player has unlocked the nightmare difficulty level
Complete any level without losing any gold from chest
Player has been hit by a homing dolphin 10 times
Player has beaten Mr. Jones in story mode
Player has beaten the second Kraken in story mode
Player has beaten the Ghost ship boss in story mode
Player has destroyed 20 enemy ships carrying gold, and picked up the gold box left behind.
Player has beaten the Skeleton boss in story mode
Player has ran into own mines 10 times
Player has beaten the first Kraken in story mode.