Hardcore mode is unlocked after completing the game once, and can be accessed from the top right option in the main menu. It requires you to play through the entire game in one sitting without dying. That's basically it.
UPDATE: No longer glitched with the recent patch!
General tips:
- Use the dpad, not the left stick. Just trust me on this, it's way more precise and you will no longer be dying cause the controls fucked up on you.
- Obvious tip, but seriously, practice the trouble levels in the main game before you bother going for this. Some parts you just have to get used to.
Level specific notes:
Act 1: Really nothing hard at all, try speeding through it if you like. I like to skip the second red cart on 4 since you have to make an awkward jump while inside it otherwise.
Act 2: Snoozefest. You have zero excuses to die here, but I wouldn't blame you for falling asleep.
Act 3: This is where it starts to get a bit dumb. Most of it is still very easy, but you really want to learn how to do each part so you don't just wing it every time. Especially 12. Practice.
Act 4: This is where most of your runs will die. The first level isn't so bad, but the rest all have scary parts. Practice the shit out of 14, you really don't want to mess up with the big wheels in a real run. 15 feels hard at first but it really isn't. 16 has that horrible air current part near the end. PRACTICE IT. Like, a lot! You won't realize how awkwardly precise it is until you get there on a Hardcore run with some pressure on you, and then you'll be glad you practiced.
Act 5: Pretty awful throughout. You need to really be consistent at everything in this act. The scariest section by far are the initial few obstacles on 19, so make sure you can do those in your sleep. 20 is nowhere near as bad as it initially seems, you just gotta get that giant sawblade descent bullshit down to a science. And then not choke there like I did once.
Have fun I guess?