Here is the full list of all 13 Draw Slasher achievements.
Master all Challenges
Play as Samurai
Kill 5000 Pirate Monkey Zombies™
Play all Arcade Modes
Obtain at least one flame in all basic Challenges
Do not kill Demon Samurai in Story Mode
Complete Story Mode
Kill Demon Samurai in Story Mode
Kill Phantom in Story Mode
Kill Hangman in Story Mode
Kill Octo in Story Mode
Kill Gunslinger in Story Mode
Kill Stomper in Story Mode