Select: Flag a Maverick as defeated. You will have all upgrades found in that stage. NOTE: There is a special case for X. You will not have the upgrades from Dragoon's stage unless you are in Mushroom, Peacock, Space Port, Final Weapon 1, or Final Weapon 2. This is to account for the revisit after Beast.
Holding L1 while selecting stage: Brings you to part 2 of that Maverick's stage. Going to part 2 of a Maverick stage will give you the upgrades found in Part 1, if any.
Holding R1 while selecting stage: Brings you to an alternative stage based on this mapping: Spider -> Intro stage, part 1 Walrus -> Final Weapon 2, part 2 Mushroom -> Final Weapon 1, part 2 Dragoon -> Space Port Stingray -> Final Weapon 1, part 1 Peacock -> Intro stage, part 2 Owl -> Colonel fight (X only) Beast -> Final Weapon 2, part 1
Note: Press select before the modifier to prevent weapon swaps, giga attack etc. from messing up saves. The combo will still if you press the modifier before select, though.
Select+Left, Select+Right: Decrement or increment the saved checkpoint. You have infinite lives, so the lives counter shows the current saved checkpoint instead.
Select+Up: Refills your health, tanks, and weapon energy.
Select+R2: Save your current hearts, tanks, armor upgrades, and current weapon. This allows you to go back to a previous item state when loading to checkpoint. A noise plays when your save was successful.
Select+L2: Load to the currently saved checkpoint. If items were set with Select+R2, they will be restored. If not, you will be given the items you originally obtained when starting the stage. Your health, weapon energy, and tanks will be refilled.
The WARNING sirens before boss fights have been removed.
In refights, capsules are not deactivated after killing a Maverick. Your character's position is slightly different after returning from a refight so as to not immediately re-enter the capsule. The center capsule is always activated.
The Final Sigma fight is infinite. Once you destroy a form, it will respawn again with full health after the next phase.
You can escape from every stage instead of just completed stages.
Loading a previous checkpoint after entering a boss room can mess up enemy textures in the stage. No intention of fixing this at the moment as it is a minor issue and likely complex.
Thanks to Luiz for doing a ton of testing, making suggestions, and providing checkpoint-related addresses.