Tor or just base Amethyst?
It doesn't seem to use much more than other social media apps on my phone, but I can try logging into your pub key to check.
Discussion
Just base, I'm not update to latest version yet. It's using around 15% battery for just 10 mins. 
This is really bizarre. 🤔
Happens to me, too, I just never thought much of it. I'm on GrapheneOS and try to be pretty tight with what I install and let run. Maybe some problematic relays in bad states or something?
It's a conflict with the rest of the spyware you have on your phone that causes Amethyst to behave in a buggy manner, crash a lot and use tons of battery. For me Amethyst runs super smoothly, never crashes, doesn't use a lot of battery; for others it's the opposite. The solution is to stop using phones.
I decide to use this phone, the battery can last at least a week :). 
I don't use other social media to check, maybe it is my phone's problem 😕
Or just a relay misbehaving and sending the same info over and over again. Any outliers in your relay list?
I will try to use bostr relay instead, only keep my inbox relays. https://video.nostr.build/b0ba8d6ac6e0157ed6a5331814eb7d476bfaa56bd872e5f067a0b87736ad2e97.mp4
Hum.. it could be. I remember that bostr had issue with auth and restarting subs. That could be it. 🤔
I've tried bostr relay, but it still use a lot battery, I will test on other phone later. 
I don't even know how that's possible. 🤔
Maybe too many decryptions on startup?