Below is a walkthrough for the Capture the Big Muck task in Rune Factory 5.
Client: Livia
Wanted: Big Muck
Location: Phoros Woods (Sighted in the northwest region)
Reward(s): Cooking Bread x1
To start this monster hunt, speak with Livia in her office at the Silo and choose the I want to check the wanted monster list option. Next, select the Big Muck from the list of wanted monsters. Also note that if you have not completed all of the 1 star monsters, then you will be unable to start this one. Travel to the Phoso Woods fast travel point then follow the path north heading towards the desert. The Big Muck can be found just past the wooden bridge over the river off to the right. Weaken it a little bit then capture it. You’ll want to watch out for the other enemies in this area. Return to Livia at the Silo to complete the hunt.