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Without knowing where exactly you are, I can only guess...

If you've accepted the task, you need to head to the blue slime forest. A new pathway has opened up for you to find. Follow the wooden boards.

As for dealing with the enemy up there... try using a careful mixture of the Resist and the Wait grapple skills. With good timing, and paying attention to the visuals, you might be able to deal a big chunk of damage.