Luck helps massively with ladder chances. About a variance of 4% for the whole daily luck spectrum(4.5 with lucky charm) and daily luck having a considerably impact too.
That being said, speed buffs will matter more than low luck buffs, unless it’s a luck buff of like 3+ then use a spicy eel and don’t bother with ginger ale unless you’re going for treasure rooms.
Go on lucky days as while unlucky days aren’t too bad they can be annoying, demotivating, and a resource drain for newer players who don’t get much from skull cavern each run anyway.
Try not to fight stuff, the more you fight the most stuff will spawn, just run around them and fight serpents if you have to. Avoid waking bats as iridium ones are menaces with the amount of health they do.
Don’t try to kill mummies it’s really not worth it, ghosts suck but sometimes it’s worth it to take a hit or two just to get them away temporarily.
Max zoom out and start breaking rocks immediately, don’t look for a free ladder, there probably isn’t one, if it’s a floor that would conceal a free ladder (long corridors) just break rocks as you walk down.
One of the biggest tips I recommend is bomb materials. You can spend a single day in the mines and get yourself maybe 250-300 iron ore and 50 coal. This will make 50 bombs but because of the resources in skull cavern you only end up with a small deficit every run. Remember to craft 5-10 bombs at a time as you go and don’t be afraid to bomb just a handful of rocks, it might even be worth bringing some copper for cherry bombs (I wouldn’t recommend it though, iron is far easier to get than copper), anything is going to be faster than the iron/gold pickaxe you probably have right now.
Try to make it down 25 levels on your first dive, that gives a 10k reward from Mr qi which I personally always use to get more food. Also try and buy some desert warp totems your first time there as 4 hours makes a world of difference in skull cavern, because of the way you generally only collect ore at the end of a run, those 4 hours can be 2-3x the amount of ore a run.
Along with crafting bombs, take all the stone you have with you, if you don’t have much spend a day resetting level 1 of the mines and break convenient boulders, that tends to give something like 1000-2000 stone a day, lots of staircases. Just place a staircase if you are in any infested floor, if you get the high spawn rate pink mist, etc. if you feel unsafe about fighting stuff. 100 stone is NOT expensive, you’re using bombs anyway you’ll get it back in a few explosions.
Don’t stand out of the way of bombs, they deal negligible damage and the ladder the bomb uncovers isn’t going to be outside the bomb radius so neither should you. Eat if you need to, there is no harm in eating more.
As we talk about eating, get used to navigating your hotbar, even the weakest foods can basically heal you from 1000 monsters attacking at once due to the game pausing when you eat and invincibility frames when you get damaged. You can outheal the most dangerous monsters with some salmonberries. Sometimes eating and running is better than attacking, especially if you know your weapon won’t cut it.
Also please don’t “fight to the death”, the monster might win and even if not another monster might snipe you. There is no reason to fight until you or the horde is dead, you can eat, they can’t. Just stop attacking, eat until you are full health, and run away or resume fighting.
Those are the biggest tips as someone who has probably spent close to 500 hours doing just combat and mining alone.