If the target creature can’t block Avalanche Tusker, but could block another attacking creature, it’s free to block that creature or block no creatures at all.

If, during the declare blockers step, the target creature is tapped or is affected by a spell or ability that says it can’t block, then it doesn’t block. If there’s a cost associated with having that creature block, its controller isn’t forced to pay that cost. If the player doesn’t, the creature doesn’t block in that case either.