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