Bear attacks siege engine (Trying to find name of anime)
This is from the anime of The Twelve Kingdoms.

The 'bear' you're thinking of is a hanyuu (those able to turn to human and back), Kantai:

 

The memorable scene of him flipping the siege engine occurs late during the third arc, A Great Distance in the Wind, the Sky at Dawn (unfortunately, I can't recall the exact episode, but it's almost certainly 37-39.)