Partial drain and refill is the only way.
I wish there was a magic chemical, but there isn’t. Lowering cyanuric acid (CYA) means physically removing some water and adding fresh water. No shortcuts.
Shock treatments, enzyme products, and “CYA reducers” are snake oil for pools. The CYA molecule is stable — it doesn’t break down from chlorine or UV light after it stabilizes. You have to dump the over-stabilized water.
How much to drain depends on your target. If CYA is 150 ppm and you want 50 ppm, you need to replace about two-thirds of the water. Test after each drain/refill cycle to see where you land.
You can buy a submersible pump or just backwash into waste. Just be smart about local water restrictions and if your pool finish can handle being partially empty (fiberglass and vinyl are fine; plaster needs caution with groundwater pressure).
Future you will thank yourself for not trying the “just add more chlorine” method.