(create your own question)How do you beat the Penguins Lair?

Take out catwomen first, after she jumps up to join penguin, batarang the two yellow conductors above them.
Penguin should get shocked and then start tossing penguin bombs at you. Use the spinner in the middle to aim the penguins at the purple machines on the floor.
When you take one out, some thugs should come out and penguin should be damaged. Keep repeating for the other three purple machines.
After all the machines are destroyed, Penguin and catwomen jump down for some fisticuffs. Catwomen can be damaged, but you should only focus on penguin because it's his health you need to diminish.
As his health starts to go down, he should start jumping up and floating with his umbrella. Batarang him down for a hit or two and repeat until he's ready for his bunk bed in Arkahm.