How about following the IFIXIT guide here: [guide|21745|iPhone 5c Battery Replacement] and all you'll need is the new set of adhesive strips: [product|IF124-015|iPhone 5s/5c/SE Battery Adhesive Strips].
Swapping out the battery is a lot easier than trying to swap out the logic board! All you need to do is find the pulls and the battery just falls out! Here's a vid that shows how you release the strips: [https://www.youtube.com/watch?v=HJ9RZt0_qMk|How to use Command™ Picture Hanging Strips] jump to time-point 1:00 where the wall part is removed. It's the same here.