You need to figure out what that bear from before is up to. Go over to the crack in the wall and head inside. In this area, watch out for the black bubbles rising, as these can hurt you if you hit them. Go from spire to spire until you get to a hole you can crawl through. On the other side, you can either bypass the guards by climbing a pole and using the ropes to get across the bridge, or you can simply use the Triangle and Square combination to take them out (hopefully you have the Silent Obliteration technique from ThiefNet).
To progress farther, use the log on the left side, then climb the rope. You now need to use the icicles hanging to get to the next area, but note that you will keep sliding down, so keep holding up. When you get to the next platform, you'll see a cutscene with a prehistoric raccoon! Bentley suggests that you help him, in the case that he might be Sly's ancestor.
Use the rings to swing across, then climb the rope and icicle, jumping to the rope to slide down. The Grizz has a key, which likely unlocks the door leading to the tiger skin you need. Wait until he runs away and back to the painting, then use the icicle to slide down and pickpocket the key. Open the door and grab the Sabretooth costume.
Go down the path leading away from this room, using R2 and X to jump the large gap, hitting the statue. Use the same move to take out the enemies, then jump the next gap. Switch back to Sly and climb the icicle, then jump on top of the cage. Jump onto the next platform, then use the costume to jump the large gap. For the next part, you need to use the hooks and spire to get across the lava, keeping an eye out for the bubbles. Use the costume to jump to the enemy, being careful of the bubbles that pop up.
Bentley says that the guards on top of the platforms are the ones restraining your possible ancestor. Use your Cyclone Pounce to get from platform to platform and take out the enemies. Make sure you watch out for the lava bubbles and once you take out all the enemies, a cutscene will play and the mission will be completed.
