Having just completed the new 'Path of Pain' portion of the White Palace, I figured I would leave a few general tips for the platforming nightmare we've been graced with. You don't really need Hiveblood, they give you practically infinite soul via statues. I still recommend Deep Focus + Grubsong for the few parts without the statues, but you can probably just farm soul off of Wingmoulds. DO NOT USE GRUBBERFLY'S ELEGY. The extra soul from the Grubsong synergy is unnecessary, and the beams make pogoing off enemies (which is necessary) next to impossible.
Longnail and Mark of Pride are massive benefits since they significantly increase your margin of error when pogoing. Just be careful not to go too early or you'll hit the roof (which, naturally, is covered in spikes). Remember you can pogo off spikes and saws, as well as enemies. Do so at every opportunity (unless it will kill you obviously). Rapidly mashing the Crystal Heart button can let you slow your wall sliding down to a crawl without needing to launch yourself off the wall afterwards. This can be very helpful when you need to wait for a saw to go past you and you don't have space to jump.
There is at least one section where you can skip the initial step via Crystal Dashing. There may be more that I didn't notice, so keep your eyes peeled. If your spawn point is next to one of the statues, heal up after each attempt. You don't want to end up somewhere you can't refill your soul and you need it. A lot of the gaps are a bit wide, so Sharp Shadow may be useful to make them easier to cross, just keep track of when a dash will be a Shade Cloak dash vs a regular one.
Path Of Pain Hollow Knight Location
There are no benches in the Path of Pain, so make sure your charm setup is able to handle whatever is thrown at you. There is combat, so don't pick charms for solely platforming. If you die here you'll have to start over (I assume).The Path is located one room up from the elevator, the left wall immediately after the room transition is breakable at the top.Hope someone finds this useful, and Good Luck!