1. Hold down either ctrl key.
   
2. Look in the upper right corner of the screen.
   
3. Press the number key corresponding to the option you would like to activate.

When active, the menu looks like this:

They're all fairly self explanatory, thanks to their helpful labels, but here's a rundown of each one.

Teleports you to the location of your (invisible) mouse cursor, ignoring collision.
(Revised description thanks to insight from General Bob in the comments)

This must be used on the main menu, unlike the rest of the options.

As it says, this resets your progress in the singleplayer/coop mode, removing all unlocked stages/weapons/etc.

Walk near a level on the singleplayer/coop map screen, then activate this. Depending on if it is already unlocked/risen/destroyed, it will move the level into its next state, allowing you to progress past it, regardless of whether or not you beat the level.

Honestly, I'm not far enough into the singleplayer to know what each of the weapons does, but this one apparently gives you a fast sword.

If I had to guess, I'd say that this might not obtainable through normal gameplay, since it's located outside of the "Unlock All Weapons" cheat, but I can't claim to actually know that, haha.

Again, I'm not sure what this does for you since I don't want to spoil my singleplayer experience (beyond deleting my progress after messing about with these for a bit), but it replaces your bullet's sprite with a shuriken.

When used inside of a singleplayer/coop level, this quickly resets it without the need to return to the map screen.

When used on the map screen, it moves you to the nearest level. (Even levels that have not been unlocked)

Plays a "YOOOO!!!" sound effect, and temporarily unlocks the other 3 weapons for use in singleplayer, coop, and versus! These weapons add even more variety to your VS matches, since they all handle very differently.

Once activated, press the upper face button (ex. triangle on a DualShock) and run into the weapon you want. IIRC, this can only be done in the VS lobby, character select, and coop map screen.

Did you lose your curse after failing a level too many times (I definitely have!)? Well, here's an easy way to get it back.

This replaces all enemies with harder versions and gives the player a nifty trail effect.

For all I know, this might not stay in after Early Access is over (or, y'know, the next update comes out), but I love it when stuff like this is included in a game. Giving players the option to tackle singleplayer content however they would like is awesome. I know I wouldn't have spent nearly as much time in Doom or A Short Hike if it weren't for the fun added by their cheat codes.

I mean, this might be a bit easy to access, but thanks to everything being labeled nicely I don't think anyone is going to accidentally erase their save, and if they did, they could get most of it back easily with these codes. (I'm not sure about weapon unlocks, and cursed level completion cannot be restored)

These may be mundane by cheat code standards, but being able to make a game easier or harder is always a good thing.

Read Trylobot's guide (found here) to learn how to access the hidden dev console, level editor, and more!