To upgrade your Battle Hall, you need War Manuals.
With each upgrade, you need more War Manuals.
Below is a list of possible ways to gain these.
Gems
You can purchase War Manuals using gems.
1 War Manual = 15 Gems
10 War Manuals = 125 Gems
100 War Manuals = 1,154 Gems
1000 War Manuals = 10,000 Gems
Campaign Elite Sweeps
You can sweet elite campaigns to pick up extra War Manuals.
Elite 5-1
Elite 5-2
Elite 5-3
Elite 5-4
Elite 5-5
Elite 5-6
Chests
Defence Chest from the VIP daily clan gifts (Anthropos city) gives War Manuals too.
VIP Daily Clan Gifts
You can collect 5 War Manuals per gift from daily VIP Clan gifts (Once you have level 25 diplomacy for this city).