After you trap Guard Slip'kik in ice, climb a ramp to proceed to the next area. On the first balcony you will see an Ogre Tannin Basket on the left side in the back of the room. This basket contains the Tannin.
As soon as you grab the Tannin, a Gordok Bushwacker will appear and start attacking you, so be prepared.
When a player picks up the Tannin, an ogre will say: "It puts the tannin in the basket or it gets the mallet again!" which is a reference to the movie Silence of the Lambs.