Hint Penguin Set!!!
All u need is finish the 3rd level. Once done, take off all your set (to die easily) and go on with the mission.
Note: You need only to die here 'coz the mission says explore! NOT defeat the boss!!! (also works in champion mode)
You'll only need to enter the dungeon 6x if you'll start with champion mode (mission for dungeon; not in champion mode is credited)
This is tested and works, I've tried it myself!!! Try it and you'll see the results.
Thoug you'll be having a bit hardwork in opening your 3rd level Altar dungeon, but its a pay off ^^
GOODLUCK Hope i helped!!!