These are ALL unlocked by doing certain tasks in the game. Chapters can vary depending on what you have previously done.

Unlock Chapter 7 Side Quest:
In less than 15 turns finish Chapter 7.

Unlock Chapter 13 Side Quest:
Go to the north western village on Chapter 13.

Unlock Chapter 16 Side Quest:
In Chapter 16 Keep one green soldier alive.

Unlock Chapter 18 Side Quest:
In less than 16 turns finish Chapter 18.

Unlock Chapter 22 Side Quest:
Recruit Hawkeye in Chapter 22 and have him gain 700 Experience Points.

Unlock Chapter 23A Side Quest:
Lord's level sums equal 49 or less.

Unlock Chapter 23B Side Quest:
Lord's levels are 50 or more (Chapter 23b will allow you to recruit a new character).

Unlock Chapter 25A Side Quest:
Level of units upgradeable via Guiding Ring/Hero Crest.

Unlock Chapter 25B Side Quest:
Level of units upgradeable via Hero Crest/Guiding Ring.

Unlock Chapter 26 Side Quest:
In Chapter 26 recruit Jaffar and have him live.