Partial drain and refill is the only real option.

There is no chemical shortcut. You cannot lower cyanuric acid with a magic additive. The molecule is stable and won’t break down from shock, algaecides, or anything else you pour in.

The standard advice is to drain about a third to half the pool, then refill with fresh water. Test your CYA level first. If it’s over 100 ppm, you probably need a bigger drain. Some areas have restrictions on draining pools (check local rules), but that’s the move.

You can buy reverse osmosis filtration trucks that remove CYA without draining, but that costs a few hundred bucks and is overkill for most residential pools. Partial drain is cheaper and simpler.

Keep an eye on what you add going forward. Most CYA comes from stabilized chlorine tablets (dichlor or trichlor). Switch to liquid chlorine or a salt system and you won’t have to do this again.