How can I get my iPad 3 battery repaired if it's failing but still shows 80% health?

well they say less than 80%

iPad Repair and Service - Apple Support

so being 80% would still make me think about replacing it

plus the battery health is it's natural lifecycle a battery can still be defect in great many ways without it being related to it's lifecycle

For practical purposes, in lieu of replacing the battery (or otherwise repairing) and returning your own iPad, Apple usually exchange the iPad for a renewed/refurbished iPad of the same model and specification. The cost of the exchange is the same as would otherwise be charged for repair. If the exchange is solely for battery service, Apple may require the assessed battery health to be 80% or less.

As for out-of-warranty repair costs, Apple offers a fixed-price price repair. You can verify eligibility and cost for your region/country here:

iPad Repair & Service - Apple Support

If you have an active AppleCare+ plan, the cost of repair is reduced to a small excess/deductible fee.