This is an easy task and a hard battle too. First complete your requests and then refresh by going into these requests in order:

Dr. Otso's Research: Find Sue, when she asks your name, don't tell her. Just finish the request like that.
Unsealed Doors: Find Sue again and talk to her, and finish the request.
(NOTE: All requests must be cleared/finished in order for the event to continue)

Waterfall Tears: You saw Anna in the waterfall room, right? Beat her and don't go to the telepipe. Now keep proceeding the CAVE 2 and look for Kireek, fight him and beat him. Finish the request.
Black Paper: Now Kireek is in CAVE 1 now. Look carefully in CAVE 1, if you found the room shaped like an cross and has a loockd room in south, beat him and finish this request as well.

FINAL: From the Depth: Team up with Ash, when he departs. Go back to RUINS 2 and check your map. You will see two people. One's Kireek and one's Ash. Go to that room, talk to Ash and beat Kireek. And you must have one slot or more to make room with Kireek's SOUL EATER as your usable weapon.

SOUL EATER is suicidal weapon but its special is to cause terminal attack but also drains your life, best you're a human with RESTA spell. Good Luck!