Here is the full list of all 21 Monmusu Gladiator achievements.
Complete Challenge 5 or higher with Shiba Inu
Complete Challenge 5 or higher with Child of Dagon
Complete Challenge 5 or higher with Dragonewt
Complete Challenge 5 or higher with Vampire
Complete Challenge 5 or higher with Ostrich
Complete Challenge 5 or higher with Big Blue
Complete Challenge 5 or higher with Moby Dick
Complete Challenge 5 or higher with Lamia
Complete Challenge 5 or higher with Slime
Complete Challenge 5 or higher with Evileyes
Complete Enjoy or higher
Complete Normal or higher
Complete Challenge 1 or higher
Complete Challenge 2 or higher
Complete Challenge 3 or higher
Complete Challenge 4 or higher
Complete Challenge 5 or higher
Complete Challenge 5 or higher with at least 10 different Monster Girls.
Copy a Growth Card.
Lose in the first battle with Shiba Inu
Win against Vampire