I had a similar issue until a couple days ago. My battery health (iPhone 6s) was at 97% but I could see the percentage drop in front of my eyes; sometimes as much as 15% in 2 minutes. And this wasn't under any heavy use but while scrolling through Settings app etc. Other times it'd drop 10-20% at a time while watching any videos in Safari. Battery recalibrating didn't help much and it'd still shutdown before it reached 1%.
I finally had the battery replaced and all seems fine now. Now I'm at 60% after 16 hrs with almost 20 hrs of videos in Safari, a few FaceTime calls and some texts/emails. Normally I'd have to have it plugged in by now. I can't say for sure if this has started with iOS 12 but it sure is remarkably prevalent on iOS 12.0.1. Before I got the battery replaced, I thought the issue has to do with how they (instantly) raise the CPU clocking in iOS 12 and that it must not have been optimized for older devices. But now my theory is that iOS, for some inexplicable reason, is unable to manage the voltage in the installed batteries.
And before anyone gives me all the "set up as new" nonsense, I already did that and my settings are pretty battery conservative with Background App Refresh OFF and Location Services only to While Using etc.