Minecraft wiki entry for Ultra_hardcore_survival, associated text: Lava is way too easy to fall into, and with no regeneration, you will die quickly.
If you are not looking, you can walk directly into fire, which never burns out on netherrack.
As fire damage can easily be a death sentence be sure to take a cauldron and a couple buckets of water with you, you can extinguish yourself by jumping into a cauldron filled with water.
Be watchful for sharp drops, and never dig down. Many floors are only one block thick, with the sea of lava directly underneath.
Wear at least one gold armor piece, so piglins are not hostile to you.
If you are having trouble finding gold in the overworld, you may also find it in the Nether in the form of nether gold ore, which can be used to make a pair of boots or golden apples.
Do not attack zombified piglins. Doing so will cause all others in the area to swarm you, which can easily lead to death.
Ghasts can quickly kill you, as well as blow out your portal. Surround your portal with cobblestone, and listen for their noises. It is easier to play with subtitles on.
In a pinch, smelt netherrack into nether brick. It will not be destroyed by ghast fireballs.
Find some warped fungi, so if you encounter hoglins you can scare them off by placing one on a nylium block without taking damage.
Remember, on your first visit your highest priority is to find a fortress to gather at least a single piece of nether wart (maybe some soul sand or soul soil to farm on) and at least two blaze rods. Opening up brewing makes future trips much safer with the likes of Fire Resist/Health potions. You can also bring water, bottles and ingredients with you and start brewing in the nether to farm more blaze rods safely without having to go back.
Remember to block off the ceilings in the fortress so wither skeletons cannot reach you. A single hit from a wither skeleton on unenchanted armor drains more than half of your health bar.
Explore bastion remnants only if you have very good armor and regeneration supplies, because piglin brute attacks can be deadly. A bucket of lava is recommended to finish them off while ensuring your own safety by towering up.