In the Treno weapon shop, monsters kept beneath the floor can be battled for rewards. On Disc 4, the purple Behemoth monster is the challenge available to the player. This achievement will be earned if you can defeat the monster using Dagger.
A dangerous and powerful monster for any character, Behemoth is especially difficult to defeat for a character such as Dagger, however there is a loophole; Behemoth is not immune to the Death status. The item Dark Matter is available in the Treno Auction House, just up the street from the weapon shop. This item will teach Dagger how to summon Odin, who can deal Instant Death upon enemies he is summoned against. The odds of him being successful are dependent on the number of Ore you have in your inventory, and is calculated thusly;
Chance of Success = (Ore/2) + Level + (Magic/4) - Target Level.
so the more Ore you have, the better. You may fail this a few times, but if you keep at it you will succeed. High speed and evasion are helpful, anything to allow you the opportunity to perform the summon will help.