First use Chilla to shoot ice spikes into Queen Thyra's eyes (they will be green when open), causing dozens of green eyes to fall out. Use 40 Below's Wrecker attack to knock them all off the platform. Repeat until you destroy all the small eyes. Queen Thyra will then open her large eye. Hit it with an ice spike then knock it off the edge with the Wrecker attack.
You have to be in Co-Op mode for this achievement (can be done in Split Screen, System Link, or Online Co-Op). This achievement can be easily completed with a second controller. If your second character dies, they will just respawn, and if your first character dies, they will respawn by the second.