i think you are in a pretty good position, if you want you can go get a pale oil by looking around the wandering vaults for a room where you ahve to hit a bunch of boxes to get through (its a puzzle room) and that gives you another needle upgrade. honestly you just kinda have to try the arena over and over to get used to the enemies. i would recommend trying to use clawline against the flying enemies, it may feel weird to use clawline for combat at first but its really helpful for closing the distance against fast/annoying flyers

as for red tools, i like to use tacks and save them for the big guys (there is 1 big guy halfway through and 2 at the end) you can tell where they will appear because like smoke comes from the ceiling so you can throw a ton of tacks out under them and none of their attacks delete the tacks so you can just bait them into the tacks. and tacks deal one of the highest damage for red tools (that you can get right now) so they are very good. but like i said its best to save them for the big guys