Niffelheim

Bears are one of the random animals that spawn on the surface at night. They have much more health compared to the Wolf and the Boar but not more than the Buffalo. You probably will know it exactly when you see it but just in case... this is what they look like:

You want to make sure you're at least on Titanium or Steel grade weapons before going up against any of the animals. While you can take them down with Iron weapons, you'll still take a pretty good beating while you do so. You also want to make sure you have a shield equipped so you can block the Bears attacks (it'll reduce the damage down from 16-30 down to 1-2). With that being said, however... it's highly recommended you work on this trophy after you have opened the Portal to Asgard. You get an incredibly powerful Sword when you do so that will easily kill any bear you come across.

Since the animals that spawn are random, you'll need to keep an eye out for the Bears to make sure you kill 10. As long as you're keeping an eye out for them, you should be able to get this trophy before you reach 100 Days played. If you don't have it by then, you'll need to keep roaming around at night to try and get the last you need to spawn. Be sure to check all 4 Lands for the animals, not just the one your Castle is located on.

After you've killed your 10th Bear, the trophy will unlock.

Note: When you unlock this trophy, you'll also receive the actual animal-head trophy for your throne room.