Once again you will have to return to the Torture Chamber, the central room of the museum. Jump down onto one of the floating platforms and use the Grapnel Gun to move west #1. Get ready, as in a few moments you will be attacked by Tiny, Penguin's pet-shark. Start rhythmically pressing X #2 to defeat the beast.
Now you can finish going west and afterwards use the Grapnel Gun to reach the upper balcony #1. Go west and soon you should reach a door leading into the Iceberg Lounge #2.
Head to the middle part of the room and get ready, as Penguin will soon start attacking you #1. As you need to approach him first, choose one of the side corridors. Evade the places where the balconies are #2 to avoid getting him with the Freeze Gun.
Your objective is reaching the western part of the room, from where you will be able to get to Penguin #1. Equip the Disruptor and wait for Penguin to decide that he's going to try his luck and let you attack him #2.
Quickly choose the corridor leading to Penguin and stop around the middle #1. Aim at Penguin and keep holding the right trigger. Don't let go until the Freeze Gun gets turned off #2.
You can now approach Penguin #1 and lead out an attack which he won't be able to dodge. A cutscene will start, though don't think you're done with Penguin. Before you can finally get rid of him, you will have to fight rightful boss - Solomon Grundy #2.