The only justification for replacing a battery on your own is if Apple no longer services that Mac, leaving literally no other option.
Batteries - Service and Recycling - Apple
Apple charges $129 for MacBook Air battery replacement, plus tax. I understand things like VAT can be expensive, but you would have to pay tax for aftermarket batteries too. Quality aftermarket batteries from reputable vendors are no less expensive anyway.
If you can have Apple replace it, definitely have Apple replace it. They will perform a thorough diagnosis to make sure the battery is in fact defective and needs replacement, and the problems are not being caused by something else. They will also guarantee their work and provide a warranty.