Robin has the acrobatic ability to swing to high places using the poles that stick out of the walls. To turn Robin around just tap on him, to make him swing in a particular direction you have to hold one finger down on him and then press another finger on the screen where you want him to go.
Defeating Harley Quinn
At the start of the game use your Batarang in the first stage of your encounter with Harley Quinn to stop her mallet-swinging attack. Drag your finger from the Batarang icon to Harley Quinn while she is spinning around to knock her down. Then in the second stage of the fight fire your Batarang at whichever fuse box she is nearest.
Equipment
Whenever you see a blue outline circled on the floor it indicates that there is a piece of equipment nearby you can use. To manipulate the equipment you just have to be stand in the center of the circle and tap it.
Extra Rewards
You can earn bricks by smashing up things in the scenery, if you gather enough bricks you will receive extra rewards.
Gold Bricks
Below is a list of Golden Brick packs that can be purchased from the in-app purchase store and then used to get the various boosters in the game.
Stack of Bricks (5): $0.99
Pile of Bricks (20): $2.99
Crate of Bricks (50): $4.99
Cave of Bricks (125): $6.99
Objects
There are certain objects that can only be handled by a specific character so you may have to switch the character you are using to progress.
Switch Characters
You can always switch characters to a super hero that has a special power or ability more suited to the level if you are struggling.
Acrobatic Robin...