Partial drain and refill is the only reliable way.
Yes, that’s it. No magic chemicals, no “natural breakdown” if you’re patient. Cyanuric acid doesn’t evaporate, doesn’t filter out, and doesn’t degrade with normal chlorine use. Once it’s high, water exchange is your only real option.
You can buy “CYA reducer” products — mostly enzymes or bacteria claims — but they’re expensive, slow, and work poorly in practice. I’ve never seen someone get a meaningful drop without draining at least some water. Save your money.
Most pool stores will test for free and tell you your CYA level. If it’s above 80 ppm (or 60 if you’re using non-stabilized chlorine), you need to lose some water. Drain a third to half the pool, refill with fresh water, retest. That’s it.
Check your local regulations first — some places restrict draining due to groundwater or sewer rules. But for the chemistry, it’s the only play.