These are the rewards for playing other games and they're permanent I believe. They include a bunch of tickets, so those are worthwhile if you can aim for them. Mission 17 rewards an L ticket, but those are relatively high difficulty challenge missions.

>Aigis
1. Complete chapter 2 story mission Protect the Temple
2. Complete Katie's Tactical Training Quest How to Fight Strong Enemies
3-5. Level a unit to level 10/30/60
6. Raise a unit's affinity to 100
7-8. 1st/2nd Awakening a unit
9. Complete chapter 2 story mission Recapture the Royal Castle
10. Complete chapter 6 story mission Demon World Baptism
11. Complete beginner gold daily quest
12-13. Complete Divine Beast Sphinx Advent Battle Intermediate/Extreme
14-15. Complete 1st/5th floor of the Tower of Heroes
16-17. Complete Amon Advent Battle Level 1/10
18-20. Reach rank 20/70/100

>Castles
1. Complete 6th Story Mission Giant Helmet Appears
2. Complete Tutorial Mission How to Acquire Ki
3-5. Level a Castle Girl to level 10/30/60
6. Raise a Castle Girl's affinity to 100
7. Renovate a Castle Girl
8. Limit Break a Castle Girl
9-10. Complete 15th/30th Story Mission
11. Complete Storehouse Defense Battle Divine Maiden 1
12-13. Complete Enma's Arena Floor 1/3
14-15. Complete Taira Corridor Room 1/5
16-17. Defeat Advent of the War God Maeda Toshii Normal/True
18-20. Reach rank 20/70/100