Once you exit the Final Offer, you will encounter the messages from Anarky. He will tell you that there are three bombs around Gotham and that you need to find them. To reach Anarky, you will need to go to the three bomb sites and defeat the gang of enemies at each within a set time limit.
Once you have defeated all three crowds and bombs, you will then need to head to the Abandoned Courthouse to face Anarky.
Once you enter, you will have to fight two crowds of enemies before you can get your Bathands, but he will join the fray soon enough. The first group of enemies will be the regular punching and bat variety. Once they are down, and second group will jump in while Anarky tosses molotov cocktails from the balcony. Watch the red icons to see where the bombs will be landing and dodge out of the way.
Once the second group of enemies is down, Anarky will then jump down and be susceptible to your pulverization. A few other enemies will join him, but unlike the Shiva battle, this fight will be over once you defeat the other enemies instead of Anarky himself. When the other enemies are down, simply pop Anarky one time to drop him for good.
For more tactics here's our full Batman: Arkham Origins boss guide!