Decided to try and level up a few times before attempting Death again, and also found some Chain Mail (which was better than my armour at the time), and realised that equipping two Cursed Rings would boost my strength and defense hugely (although my luck would drop – not important for a boss fight though, I don’t think). I also found a HP Max upgrade too, which would help.
It still took me five or so goes to kill Death, although it was his second, skeleton crab, form which was difficult. Thankfully, the axes I’d found really helped, as so I killed him eventually – that’s the second Death today! I got a power-up which “cleanses water”, so no doubt that means the acid water I couldn’t get past before is now clear for me to touch.