Titan Tokens
Champion Monsters currently drop Titan Tokens, which is an in-game currency. These Titan Tokens may be vended, traded, put in storage. There is no way to get these tokens by donating. You must either kill the monsters, trade for them, or buy them from a Merchant's shop.
10 Titan Tokens can be exchanged for a Costume Egg, which will give you a random costume headgear. To exchange your Titan Tokens for a Costume Egg, open the Titan Guide in your inventory, and select the appropriate option. The Costume Egg also has nice descriptions of the possible headgears you can get.