Hey so i just did the speedrunner achievement and wanted to make a guide because this great higher quality guide helped me get the achievement in the first game, also this game is so incredibly beautiful and it's everything on my mind rn. My run was pretty close but i wasted like an hour on an arena because i completely forgot about the pinmaster and didn't buy bell stations. All to say the time limit is pretty generous and i think if u beat the game you can probably do it.

just in case

This route isn't very optimized for comfort so grabbing some tools or a skill on the way will make the run easier i'll mention some i thought of after doing the run but i haven't tested them. Let me know if u have suggestions for upgrades to put in the route.

Did a second attempt to show that there is quite a bit of spare time. I still had plenty of deaths and its by no means a speedrun but i wanted to show that i really did just waste 1 hour on that arena.

1. Play with bell beast
   
2. Get Dash
   
3. Defeat Lace
   
4. Get Hover
   
5. Defeat Moorwing
   
6. Get Claw
   
7. Defeat Widow
   
8. Defeat Cogwork Dancers
   
9. Get Melodies
   
10. Defeat Lace again
    
11. Defeat Grandmother Silk

Path order is:
Red > Dark Blue > Yellow > Pink > Green > Light Blue > Yellow again > Purple > White
sorry for using Yellow twice i forgot i already used it at the start
I'll mark optional Benches with an O on the route and arenas with an A.
The achievement goes by ingame time so you can pause the game and take breaks (map and inventory probably count aswell)

1. Get to Bone Bottom
   
2. Get Silkspear

O: Bench
1. Defeat Bell Beast

O: Bench closer to Dash (arena ahead)
1. Get Dash

O: u can bench closer to Lace but its locked behind an arena
1. Defeat Lace

(thx to King Ultimax in the comments for suggesting the Craftmetal)
Warding Bell is a good defensive option and the Craftmetal can be used to get 4 tools on the way (2.5 of which are usefull imo).

1. Get Warding Bell
   
2. Get Craftmetal
   This can be used to get either the Cogwork Wheel or Sawtooth Circlet at the Twelth Architect or later on in High Halls to craft the Cogflies if you don't have enough rosaries for the other two.
   
3. Continue to Seamstress
   

1. Talk to the Seamstress and accept the wish
   
2. Farm the spines then quit to bench (u can respawn the enemies that drop them by exiting and reentering the room at the transition to the right)
   
3. Get Cloak

1. Defeat Fourth Chorus and go up to Greymoor through Pilgrim's Rest

Getting Thread Storm and Threefold Pin provides more offensive options. Thread Storm is good aoe and helps with arenas and Threefold Pin is good dmg against bigger bosses (beware of shell costs tho).

1. Bench at Shakra (arena ahead)
   
2. Beat the arena inside the Craw Lake building
   
3. Get Thread Storm
   
4. Get Threefold Pin
   O: Bench at the Bellshrine

1. Bench at Halfway Home (arena ahead)
   
2. Unlock the shortcut
   
3. Defeat Moorwing

1. Bench at Bellhart (arena ahead)
   O: There is an enemy pogo to skip Sister Splinter (example video)
   
2. Get Claw

1. Defeat Widow
   
2. Buy the Bellhart Bellway station
   
3. Get the first nail upgrade

1. Unlock Elevator
   
2. Bench at Halfway Home for Sinners road
   O: Unlock shortcut
   
3. Solve The Mist
   
4. Bench inside of Exhaust Organ top left
   
5. Defeat Phantom

1. Bench at Grand Bellway and buy the station if u can't there will be another chance later
   
2. Bench at Songclave
   
3. Defeat Cogwork Dancers
   
4. Unlock the lower door
   
5. Unlock the upper door
   
6. Get Pale Oil

1. Bench at Grand Bellway and buy the station if u didn't earlier (farm rosaries in the room to the left of the station if u can't afford it)
   Travel to Bellhart and get the second nail upgrade
   
2. Defeat Trabbio back at Grand Bellway

1. Bench at the Architect
   
2. Get Harpoon
   
3. Take the path below elevator

1. Bench and get the Sacred Cylinder

1. Get the 1st melody (give cylinder to collector)
   
2. Bench at Songclave and make your way to High Halls

1. Bench infront of High Halls
   
2. Bench after High Halls (arena ahead)
   Beat the hardest Boss in the game this arena took like 1 hour without any nail upgrades gl
   
3. Get the 2nd melody and follow purple path back to Dancers

1. Bench below Cogwork Dancers
   
2. Solve Core "puzzle" and get the 3rd melody

1. Bench below Cogwork Dancers one last time
   
2. Defeat Lace again

1. Bench at Terminus
   
2. Unlock shortcut
   
3. Defeat Grandmother Silk

Hope this helps some people if you have feedback let me know.
GL on your runs!

Guide inspiration: Hollow Knight - 5 Hour Speedrun Achievement Guide by fireb0rn
Full Map image: Post by u/Zignixx
Sister Splinter skip: Video by DuoRue