It took me a little time to develop a proper sequence of actions based on Joker's behaviour but then it became very easy to complete.
Battle is divided on 4 stages - each time Joker behaves differently.
You have to beat Joker 7 times - twice for each stage except the 1st one (single hit is enough for it).
In general, Joker always tries to be at the opposite side of the battle ring - you have to chase him to shorten the distance and hit him.
*** Spoiler - click to reveal ***
1) Beginning. Just use your line launcher immediately and hit Joker for the first time.
2) Joker starts to use his revolver. To avoid being shot use A+A when the aim is almost ready. At the first half of this stage (before you hit Joker for the first time) the aim is getting built slowly, so you have much time to react. At the 2nd half the process is much faster so you have to evade immediately after aim indicators appeared.
Each time you evade you should shorten your distance to Joker, but not too much - he will perform unavoidable melee attack if you will be too close.
After 3 consequitive shots Joker starts to reload (but if you got shot once the 3-shots sequence will start over again).
That will take like 5-10 sec - he will stop and won't react on your movements. This is the TIME. Run and hit him. Repeat that again (with faster aiming/evading) to switch to the next stage.
3) Joker starts to use its electric rod. Now it's his turn to chase you. When the rod is charged he runs to you to perform a melee attack. Just use you quick batarang (I've got already electrified upgraded version - don't know if original version will work) to disrupt rod's charge and stop Joker. That will force him to esape you again on the opposite side of the ring. Then he will try to reanimate his rod. Just wait for that moment and again - run and hit him. Repeat that twice (there're no changes in Joker's behaviour at that stage).
4) Now it's a mix of stages 2 and 3. Plus this time Joker puts a gas mask and opens gas containers, so now you have a limited time to perform two hits before you will start to die beacuse of the poison.
This stage is a little bit tricky. Joker uses both the gun and the electric rod so you have to manage a moment when both of them are disabled (rod is de-charged and the gun is empty). So be ready to evade and use your quick batarang at any time. The second problem is that Joker's pause time intervals are now shorter than at the previous stages so it's very hard to reach him actually + (remember?) you have a real shortage of time because of the gas.
My solution is to use explosive gel now to disrupt Joker's movements what will allow you to reach him comfortably. Use some opportunities at the previous stages to land 3 portions of explosive gel at some points, not too far from each other - just at 3-4 steps distance.
Now take your time to disrupt the rod and empty Joker's revolver to force him to pause for reloading. Try to get that in such way that he will be close to the first portion of gel. Now chase and beat him for the first time. After he's recovered he will try to escape you, so that's the time to explode the gel. That will disrupt Joker and you will be able to beat him down 2nd time immediately. Otherwise, he will escape you and you probably won't have enough time to empty him again - you will suffocate.