Mansion Entry Hall - Batman: Arkham Asylum
As you pass through the door that leads to the Entry Hall you will earn the Achievement: 'Breaking and Entering' (10 GP). Ahead of you and below are three thugs – two unarmed and one armed – so go ahead and glide down there and take them out. Turning towards the front of the building you will see a security forcefield – run towards it then turn left at the bottom of the stairs, rip the grate from the wall and enter the duct to claim another Riddler Trophy!
Now head back up the stairs, then up the next set of stairs and try the door there – nope, it is locked! Well that's okay, we'll just zip up to the platform above this door and pull the duct grate off of the wall and zip up there – to find a weakened wall to blow with the third Spirit of Arkham message behind it – pretty spiffy XP!
As you drop down into the main room you see a large group of thugs searching through the records here – there are a few ways that you can do this, depending on your mastery of combat. Since I am into the combo system, I just glided down for a glide kick ground takedown on one of the thugs and then beat the others senseless, but if you are a button masher you may want to do glide kick ground takedowns and then retreat to the Gargoyles and rinse and repeat. Either way, once you have all the thugs down, head for the far end of the room where the twin stairs are, take the left set.
At the top of the stairs, kill the two pair of Teeth, then rip the grate off of the wall and kill the third set of Teeth inside that little room. Now go back down the stairs and rip the grate off of the base of the statue and zip up to grab another Riddler Trophy. Finally head back down the hall to the alcove on the left and turn to your left – there is a plaque of Commissioner Gordon on the wall – in Detective Mode, scan the plaque holding LB to solve the riddle.