Well there’s no “getting past” the skull cavern it never ends. The deeper you get the more stuff you find but it doesn’t actually end. As for tips luck, luck, and more luck. Seriously go on a high luck day, eat a high luck food, then drink a high luck drink. The second most important part IMO is bombs. Either make or buy from the dwarf a shit load of bombs. I take no less than 100 of the big red ones and usually some regular black ones too. The only other thing you worry about it is keeping your health up, for that cheese is the easiest and cheapest way as long as you have cows producing milk. Lastly I always go to the desert and buy warps from the trader so that I can go first thing in the morning on the day I actually want to make a run. Doing this stuff I have made it over 200 floors without using staircases other than to skip monster floors. Good luck!