Taken from reddit /u/Zentori

Complete all of this week's Master Missions

Defeat 3 Saber, Archer, or Lancer-class Servants

Defeat 3 Rider, Caster, Assassin, or Berserker-class Servants

Defeat 15 Heaven attribute enemies

Defeat 30 Heaven attribute enemies

Acquire 2 Blue, Red, Gold Gems or Pieces/Monuments through battles

Acquire 4 Blue, Red, Gold Gems or Pieces/Monuments through battles

To Complete:

With Free Quests:

3 Fuyuki X-F [3 Lancer, 3 Assassin] = 18 AP

3 Septem Mt. Etna [21 Heaven attribute] = 27 AP

1 Treasure Vault (QP Daily Quest) [9 Heaven attribute] = 10 AP

Training Grounds [Gems/Monuments]

Total: 55+ AP