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