Here is the full list of all 15 Equestrian Training achievements.
Galop 1 exam
Galop 2 exam
Galop 3 exam
Galop 4 exam
Galop 5 exam
Galop 6 exam
Galop 7 exam
Complete 5km endurance trail
Complete 15km endurance trail
Complete 30km endurance trail
Complete 40km endurance trail
Grooming for a lesson
Grooming for a competition
Successfully complete show jumping Course 1
Successfully complete show jumping Course 9