I've been told that it's best to update your phone while it's charging. No matter if you're phone's at 100% or at 51%, it's better and faster if you charge it. I recommend you do this first.
If that doesn't work, try updating your phone at a different "location" where you can connect to that house's/place's Wi-Fi that hopefully has a stronger connection (with their permission, of course).
If that doesn't work either, this is the most pain-staking process but you have to update it using your laptop that has iTunes in it. Doesn't matter whether it's a MacBook or a Windows laptop, you just need the iTunes app and you need to connect your iPhone to your laptop. You should find a very small icon of a phone around the top right of your screen once you've connected them, and if you click it, there will be a clear button that says "Update" and you just need to click on that. You may need to "Sync" it first but I believe that it is all you need to do.
If it fails because the "network connection has timed out" or for whatever reason, don't panic, it just takes a few tries. It took me 3-5 times of clicking "Update" again and again before my phone actually DID update. So just be patient.
I hope this helps.