Well, this is it.
There are two sections to this battle. The first will seem very familiar. Two titan thugs and a huge number of other thugs will attack Batman. This also happens twice earlier in smaller fights and in the Bane fight, so players will probably have a good idea of what to do by now. Fight the thugs like normal. The titan thugs can only be defeated by hitting them with a Batarang while they are charging. This will send them stumbling, at which point Batman can melee them. After several hits, Batman will swing onto the back of the titan thug, allowing him to move it around for awhile and attack other thugs and the other titan. Once both titans and all thugs are down, a cut-scene takes place.
After the cut-scene Batman will be put into the ring with a giant titan-fulled Joker. This battle would probably be hopeless, but after chasing Batman around for a few seconds he hops out of the arena and pours thugs into it. Defeat the thugs. Be sure to avoid the walking bombs that Joker throws into the arena, as they'll knock Batman down and inflict a decent wound.
Once the thugs are down, use the enhanced Batclaw to topple Joker back into the arena. This takes out part of his life. He'll chase Batman around for a few seconds again before jumping back out and putting more thugs into the battle. This time some thugs with stun-guns and knives are included.
Rinse, repeat. After the third time the Joker is pulled into the arena, a cut-scene takes place. That's it. You've beaten Batman: Arkham Asylum.