Steel Soul mode is unlocked after completing the game. This is a hardcore version of the game where you have one life and do not respawn upon death. This run will be done on a separate save file where you choose Steel Soul mode at the start and if you do die, the save file is essentially deleted.
Assuming you know your way through the game, this isn't really any more difficult than a standard mode run because you can pause and quit before you die, then restart from the last bench you saved at. Almost all damage in the game causes you to lose a single mask of health and a few enemies and bosses deal two masks of damage at a time, so as long as you're careful when your health gets low death should be a non-issue.
To increase survivability, prioritize finding Mask Shards
, Charm Notches
, and Pale Ore
for Nail upgrades. The Fragile Strength and Fragile Heart charms (sold by Leg Eater in Fungal Wastes) are particularly strong since their drawback is basically nullified because of permanent death.
All that is needed for this achievement is completion of the story, which requires destroying the three Dreamers, then defeating the Hollow Knight in the Temple of the Black Egg. You'll likely end up combining this with the Steel Heart achievement, though, so feel free to refer that solution for further information: