I played this before acknowledging that GBJam was still in voting, so I'll try to make sure to play again in a few days once you've had a change to do some more updates.
You did a good job giving the game that classic Gameboy feel. The look and sound were well done, and I particularly enjoyed your box art. Your color palette fit your game well, and the cat animation was cute.
The encounter rate was insanely high. There were several times where one combat would end and another would start before I had the chance to move. At one point I had four back-to-back fights, which combined with the number of times I missed took away a lot of the fun. High encounter rates can sometimes work, but being unable to move between fights left me feeling like I wasn't achieving anything.
Talking to the witch after giving her her item gave me her thank you comments and then her asking for help dialog. When I returned to the tower, I couldn't go up to the next floor. I picked up the batteries and talked to the first person again, and when I returned to the witch she only said her asking for help text. I went back to the tower after that, but was still unable to go up to the next floor.
In the room with the batteries, when I had a fight after picking them up they reappeared and I could pick them up again. Thankfully I only needed to pick them up once, so I didn't have to hope I got out of the room without a fight, but without an inventory screen to double check made me wonder whether I had them or not when they reappeared.
I think this has potential, but needs a bit more work to really make it fun.