Here is the full list of all 15 Gladiator Trainer achievements.
Visit the Royal College of War
Defeat Emeric the Champion
Defeated the Champion of Willowsfall
Defeated the Champion of Tonstead
Defeated the Champion of Wainton
Defeated the Champion of the Dunes
Visit a horse in your stables
Defeated the Champion of Stonyford
Get married
Defeated the Champion of Sandworth
Defeat the Champion of Waldley
Defeated the Champion of Greenwood
Accepted Folke's assignment
Sanctify the crescent blade
Complete the main quest