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Quasar can manipulate anything with his power as seen in Annihilators.
Is there a way to make Hyperion jump out of the universe or will he defeat Quasar?

Going with Hype after an interesting battle.

Quasar would probably stop him cold.

Physically Hyperion should be able to wreck him but Quasar should have the tools and knowledge to give himself a pretty clear advantage I would think.

He might make Hyperion disappear.

Quasar drains him.

Hyperion might be able to fill space with a sound that can effect Quasar.
If he can mix the noises that radio telescopes have he would be able to speak in universal cortex. With enough of his perfect memory he could in effect breath destruction.