1. Get there as early as possible. Use a warp totem. Keep the TV close to the bed and a chest next to the TV.
2. Anything you want to bring to skull cavern goes in the chest. On a high luck day (spirits are very happy), you take a warp totem out of the chest, drink a cup of triple shot espresso, dump all your tools (except pickaxe and sword) in the chest and use the totem.
3. A chest next to the cavern entrance should contain a staple food (gold star cheese or salads are good), food with a buff (spicy eel for speed and luck, lucky lunch, crab cakes for defense and speed), espresso, a couple of staircases and bombs. Take 30-50 staple food, 2-3 buff food (pick one kind), 3 espresso, at least 10 stairs, at least 100 bombs.
4. Have the galaxy sword or the lava katana.
5. Eat your buffed food (drink coffee if you didn't at home) and enter.
Your goal is to place bombs near clusters of stone to find stairs quickly. As soon as you find stairs, you go down. If it's a hole, use that. Don't mine, run from enemies instead of fighting. If you enter a spiral or infested floor, use a staircase. Eat as soon as you hit half health. Check your health before using stairs. As soon as your buffs time out, eat/drink buffed food.
There's no need to go home. If you're not close to 100 at 1:30, you can leave to dump your leftover supplies in the chest. If you faint at 2am, you'll pay max. 1000G. It's worth it.
Useful rings are iridium, crab shell, slime charmer, lucky, napalm. Try it out and find a combination that works for you. Burglar is good for loot, but not that useful to get down quickly.
Instead of bombs, you can also try the slingshot with explosive ammo.
It takes a bit of training, but it does get easier over time. You can also use stairs if you want to. Jade can be replicated quickly and exchanged on Sundays.