Here is the full list of all 16 TITAN SLAYER achievements.
Clear Stage 2
Clear Stage 3
Complete the Tutorial
Clear Stage 1
Complete Hard Mode of All Stage
Complete All Stage with Hand Gun equipped only.
Complete All Stage with Machine Gun equipped only.
Complete All Stage with word equipped only.
Complete All Stage with Bow equipped only.
Complete All Stage with Shotgun equipped only.
Complete All Stage with Bomb equipped only.
Achieve SSS on Stage 1
Achieve SSS on Stage 2
Achieve SSS on Stage 3
Achieve 100 Head Shots
Avoid giant's attack 100 times