Here is the full list of all 22 Yusha Prototype achievements.
Defeat "Cyclo Gorillini" in normal difficulty or above.
Defeat "Parasitic Armor" in normal diffuculty or above.
Meet the origin of the curse for the first time and defeat her in normal difficulty or above.
Finish the tutorial.
Defeat "Cyclo Gorillini" quickly without dying in normal difficulty or above.
Defeat "Parasitic Armor" quickly without dying in normal diffuculty or above.
Defeat the heavy armored witch quickly without dying in normal difficulty or above.
Unlock the first special skill.
Unlock the second special skill.
Defeat the trainer quickly without dying in normal difficulty or above.
Defeat mecha slime "Faulty" quickly without dying in normal difficulty or above.
Defeat "Mecha Mommy Slime" in normal diffuculty or above.
Unlock the special skill from the witch herself.
Defeat "Mecha Mommy Slime" quickly without dying in normal difficulty or above.
Unlock the third special skill.
Defeat the "Old Experimental Soldier" quickly without dying in normal difficulty or above.
Defeat "Armor tank G-203C" in normal diffuculty or above.
Defeat "Armor tank G-203C" quickly without dying in normal difficulty or above.
Unlock the fourth special skill.
Defeat "The Witch of Despair" in normal diffuculty or above.
Defeat "The Witch of Despair" quickly without dying in normal difficulty or above.
Clear the first route of the story.