Felicity

Relevant encyclopedia entry: Coliseum Battles

In the coliseum, 1 to 3 of your dragons can level and fight monsters for a variety of loot. To be able to fight in the coliseum, a dragon must be 1) an adult, 2) named, and 3) fed. Hatchlings cannot fight in the coliseum, but a hatchling can become leveled if you level them as an adult first and then use a scroll of eternal youth to make them into a child again.

Dragons fight in rounds against 1 to 3 enemies, taking turns based on stats. If your dragons reach 0 health, they will pass out. If all of your current fighting dragons pass out, the match will end. You can start a victory chain if you win enough rounds in a venue befitting the level of a dragon, and can earn more experience as you do so for a maximum of +20% additional experience per fight. This is called a victory chain.

Dragons start at level 1 and can reach a max level of 25. For every earned level, your dragon gains additional health, points to use in the Abilities & Stats section, and (optionally) become worth more money when exalted. The higher level your dragons are, the more venues they can go. However, dragons will not gain experience if they venture into venues too far beneath their level.

Dragons can be made stronger by spending earned ability points and also by having battle stones added to their collection. Battle stones can be bought in the auction house or acquired in the coliseum, and can alter your dragons stats or give them new abilities.

Your most useful ally will be the "eliminate" ability, which when used correctly can one shot most enemies. It is more expensive than other battle stones, and does not drop too often in the coliseum so it is harder to come by. Most won't use put an eliminate on a dragon until it's fully leveled and "worth" it.

Similar in concept to Pokemon matchups, certain elements are stronger and weaker over others. Your dragons might have an easier time fighting certain monsters, and alternatively might struggle against different ones.

Dragons who reach level 25 are often used to farm certain venues, or to speed level dragons in a high venue. Guides on how this works are found in the forums, with different guides for different types of "builds" depending on what you want your level 25 to be.

Leveling Guide:
1 to 25 leveling guide (NOTE: rather old, but still more or less useful)
Battle Stones and Builds

As added fun, if you're looking to spice up the coliseum there are plenty of coli-based challenges in the Quests & Challenges forum!