1. Get the necessary supplies
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×You're gonna need ink in a vial, and some paper. You got paper ages ago (note from the librarian), and the ink is in the vial in the adventurer's guild.
2. GET DAT CAT
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×You need to get the cat out of the tree. A high-level rogue may be able to sneak up on it before it climbs. Or perhaps animal ken helps? Or you can feed the cat - cats like fish.
Warrior can fish at the lake using the net from the boat.
Sorceress can do the same, but must cast Blessing first.
Rogue I dunno, steal some fish I guess?
Offer fish. Then you can pick up the cat.
3. Cat's out of the bag
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×Bring the cat home, to Munavagir. Now you can use the ink on the kitty's paw and get the pawprint (the cat's footfall) on the paper. As a bonus, the librarian will now vouch for you because you brought the cat home.
You can trade the Cat's Footfall to Eitri for the flowers.