After you enter shadowthorn, walk west until you find a ladder to go up.
Walk south-west and you will end up in a room with 2 ladders, go down.
Now head south-east into the tower and go down the ladder (if you go up, you can do the Dragon Tower Quest).
You will be in an underground area, start walking west and eventually you will see some stairs to go down.
It can be a little difficult to clear this room for lower levels. You should try to stay close to the stairs because if you move further in the room you will be attacked by a few more monsters and that will make things a lot harder. You could also use a Stealth Ring or the Invisible spell to avoid some damage.
In order to get your rewards just walk a few steps to the north and you will find it inside the 3 Chests next to the wall.
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