If you can't mill a card, you'll still follow the rest of the instructions of Ursine Monstrosity's last ability.

Ursine Monstrosity must attack the chosen player if able, not a planeswalker they control or a battle they protect.

The card types in Magic include artifact, battle, creature, enchantment, instant, kindred, land, planeswalker, and sorcery. Legendary, basic, and snow are supertypes, not card types; Horror and Room are subtypes, not card types.

If, during your declare attackers step, Ursine Monstrosity is tapped, is affected by a spell or ability that says it can't attack, or hasn't been under your control continuously since your turn began (and doesn't have haste), then it doesn't attack. If there's a cost associated with having Ursine Monstrosity attack the chosen player, you aren't forced to pay that cost, so it doesn't have to attack that player in that case either.

If your turn has multiple combat phases, Ursine Monstrosity's last ability triggers at the beginning of each of them. Ignore any choices made for its last ability during previous combat phases.

If Ursine Monstrosity isn't forced to attack the chosen player for one of the above reasons but can still attack, you may choose to have it attack another player, a planeswalker, a battle, or nothing at all.