Ok, see if any of these suggestions help: https://support.apple.com/en-us/HT201412.
Sometimes a low-maximum-charge-capacity battery may impact phone performance, so see if you can replace your battery first.
But at that price, it seems like Apple is charging you for a motherboard replacement, which means that something inside the motherboard has went wrong (e.g. water got in, short circuit, a broken IC).
Unfortunately, if you have tried all of the steps above but nothing works, you will have to pay that price to Apple so that they can fix your phone and 'revive' it. You can find an Authorized Service Provider though, which some have prices that are slightly cheaper than Apple's official repair pricing.
You can find one when you select the place to repair your iPhone when you reserve a time slot for the repair.
Hope this helps!