The fastest run on hard mode (singleplayer) is on YouTube, though not labelled as a speedrun. Based on the video timer, kb has the hard mode record with a time of 50:29. ()

There is also an amazing Platypus player on YouTube; Andrija Olujić. I believe all their non-segmented runs of the game were done on hard, but if not, they would likely have the normal mode record.

As it stands though, the normal mode record is free to pick up.

(Will update if new information is found)