If a creature can't block Treeshaker Chimera for any reason (such as being tapped), then it doesn't block. If there's a cost associated with having it block, the player isn't forced to pay that cost, so it doesn't have to block in that case either. If there's a cost associated with having it block Treeshaker Chimera, but not to block other attacking creatures, that creature is free to block one of those other creatures or to not block at all.

If a creature is required to block two or more different creatures, its controller chooses which one that creature blocks.