As
@Lew Zealand said, using staircases is the easy way out (or down). The.. hmm.. feedback once you get to level 100 is cooler if you get there the "honest" way with under 10 staircases, but at the end of the day it doesn't matter.
Go on a max luck day, and have 2-3 Spicy Eels and a handful or so of Triple shot espresso (both can be traded for in the desert). Use a desert totem to get to the desert 4 hours before Pam. You can buy them from the desert trader on any day for 3 omni geodes each. It's definitely possible to get to level 100 without staircases (or very few) while taking the bus there, but it's easier if you have 4 extra hours. High luck from a max luck day and luck food means you will more frequently find ladders, holes and treasure rooms, all of which make the descending easier, especially the holes you can jump into. Make sure you have healing food too, that does not overwrite your speed and luck boosts. An Iridium pickaxe is basically twice as good as a golden one, but if you don't have that, a golden one is okay too. You're bound to find some iridium ore while going down, even if you fail to get to level 100, and that will soon enough enable you to upgrade to an iridium pickaxe.
The reason I prefer speed from both coffee and spicy eels (they don't overwrite each other, because they come from two different categories: food and drink), especially when mining a lot with the pickaxe, is that then you can move around much faster, and even largely ignore enemies. Sometimes you can even outrun serpents, but in general you need to kill off those. Just be aware that their "hitbox" is larger than you think, so it's possible to swing the sword earlier than you think, and still hit them. And conversely, they can hit you before they really "should". I find it easier to attack upwards (with the serpent above you), so try that if the situation fits. The reach of the sword appears to be less if you swing downwards for some reason. Possibly because the serpent can nibble at your ankles, while your sword is higher up, and therefore you have more reach if swinging upwards.
Whenever you find a ladder or a hole, go down ASAP. No need to wander around for ore when the main goal is reaching level 100. Try to keep your health topped up, because a couple of serpents can make quick work of you if given a chance. In single-player the time stops while eating, so it's safe to gobble down a cheese or sashimi while a serpent is bearing down on you. May just save your life. Plus, it gives you time to get your bearings, with time in practice stopped for a few seconds while you eat.
Bombs and mega bombs help a lot when trying to find ladders/holes, and also for mining purposes, but they're also expensive, so perhaps you want to be conservative. Use them on big clusters of rocks, and not in narrow hallways.
Good luck!