Main Sequence

The main sequence in a game is the normal (most natural) sequence in which required items are acquired, bosses are fought, characters are met, and major events happen. Everything listed here is required, anything else is considered optional.

A sequence break occurs when a player do things in an order that differs from the main sequence. Listed here are only the sequence breaks that don't make use of major (or game breaking) glitches (whether said breaks are intended or not).

A "branch" occurs when the main sequence offers multiple equally natural choices. (Players must complete all branches, but can do so in the order they want.) Axiom Verge 1 has no such branches. Axiom Verge 2 does.

Axiom Verge

Main Sequence

Axiom Disruptor
Nova
Xedur
Laser Drill
Elsenova
Kilver
Telal
Address Disruptor 1
(Jump of No Return)
Field Disruptor
Uruku
(Power Filter Turned On)
Modified Lab Coat
Remote Drone
Address Disruptor 2
The next four entries can be skipped with a trick called the "Grapple Skip" (see below):
Gir-Tab
Katrahaska
Repair Drones (reactivation)
Grapple
(Hallucination Sequence)
Vision
Ophelia
Daraga
Trenchcoat
The next two entries can be skipped with a trick called the "Bomb Skip" (see below):
Aborted Clone
Address Bomb
Ukhu
Drone Teleport
Sudran Key
Red Coat
Sentinel
Xedur Hul (ignore or kill)
Athetos

Sequence Breaks

In Axiom Verge, there are only two breaks of the main sequence, both of which only allows to skip a few things.

Grapple Skip

The Grapple Skip involves finding a way to get back from the "Jump of No Return" without the Grapple. This is the only, normally non-optional, purpose of the Grapple in the whole game.

There are three methods to do so:

Never enter a Rebirth Chamber to heal or save after the "Jump of No Return". Then, after getting the Address Disruptor 2, either commit suicide or "save and quit" to reappear in a rebirth chamber prior to the jump.
Clear the jump to reach Oracca without the Grapple. Normally impossible, but by sending the remote drone over the edge to go provoke a Blurst, one can use the released Blurst's Swarm to perform an insanely difficult "damage boost" to clear that jump.^[1]
Clear the "Jump of No Return" in reverse. It is, apparently, barely possible to do so with just the Field Disruptor.^{Footage wanted.} This method is much slower than the second one, but arguably easier.

The last two methods are slower but there are reasons to use them:

In a casual run, it allows to keep using rebirth chambers to heal and save.
In a speed run, it only makes sense to use them in a category where the first method is forbidden by the rules. For instance, the "warpless" category, where one can neither return to the menu or die.

Regardless of which method is employed, the player is able to make it back to Eribu, then towards the "Hallucination Sequence" to continue the game like "normal". However, because the repair drones weren't released, two story points will be messed up:

Ophelia is not supposed to be repaired and functional. She will be repaired anyway.
A repair drone comes to save Trace after the Vision battle. It won't be there. You can still hear the sounds it would make and Trace ends up being saved anyway.

Bomb Skip

This skip is rather simple. The path to upper Edin and Ukhu is blocked by Lv.3 breach, and only an Address Bomb can remove it. But, it doesn't have to be removed, actually. By taking damage and using the Trenchcoat, one can simply teleport through it. Beside that, the Address Bomb is only required for optional items and shortcuts.