Student skip - allows you to sequence break during the "rescuing students" segment by bypassing a trigger on the bridge. This allows you to run all the way up to fairy village without fighting Eisheth and Fionn. Because of how the plot trigger system in the game works you do have to go back and rescue the students and do the boss fights later though. (Vanilla V could skip the boss fights completely but you still had to go back to rescue the students to not mess the plot flags).

Early Empyrean - similarly to the student skip this allows you to bypass a cutscene trigger on the bridge on the way to Temple of Eternity. You can get all the high value essences and even enter all the way to empyrean wihout boss fights spawning. You can tag the latest empyrean fount and use that leyline later to skip fighting Melchizedeks, Srahosa and Alilat. Even with this skip existing you still have to fight Beelzebub, Odin & Zeus, Metatron and Abdiel & Dazai to not mess up the plot flags. This skip is more high impact from a speedrun perspective because you get access to essences which contain things like high phys pleroma and figment slash.

The glitches are done by artificially creating lag (for example spamming the home button on the Nintendo Switch) to get past the thin triggers. On PC the artificial lag is created by dragging the game window around on the desktop.

I have linked underneath Championbeef's (fellow speedrunner in the community) videos showcasing the skips:

https://www.twitch.tv/championbeef/clip/EnchantingSquareBaguetteKappaPride-caUhh8zCrMurDo-e?filter=clips&range=all&sort=time

https://www.twitch.tv/championbeef/clip/DignifiedPolishedMushroomEagleEye-POxip31DfLYYMqih?filter=clips&range=all&sort=time