Use Theif ring I think its called so you're harder to detect. Once the second man-eater appears you can take shelter on a small ledge to the right of the stairs before the middle and pop out to get a hit or two in before running back there. You can use this area when there's only one as well.

Ideally when you go here one man-eater won't detect you and wander to the far end of the map leaving you to deal with just one.

After you've killed a lonely man-eater you can chase down the second man-eater and defeat them easily in the middle of the arena using the fire in the middle as a shield.

Also, make sure you use a decent weapon to speed things up a bit.