Intro Stage
Note - X Armor part is in section 3
Intro - Crab 1
The first section of the intro stage is easily handled with dash jumps and X full charges.
When you get to the crab boss, keep in mind you can use both the dedicated buster and special weapon button to fire buster shots (assuming you have no weapons equipped). Use full charges on the crab's head, and add lemons in between charge shots with the alternate attack button.
Intro - Crab 2
X should leave after the first crab encounter, leaving you in control of Axl.
Unlike X7, hovering with Axl requires pressing jump again. Use Axl's hover to cross the first large gap.
Beware the enemy near the end of the section before the door if the little bulb enemy attaches - getting bodied by it is almost a one shot kill.
Encounter room
For the encounter room, get Axl onto the right ledge near the door, look left, and just hold attack. Adjust aim as needed, and kill them as fast as possible.
Grab the gems while the door is loading.
Crab 2
Zero joins before Crab 2.
The second crab is actually a tutorial for using the Team attack. The small crabs always drop team attack crystals - grab them until the meter is full. Get close to the crab's head, and use the Team Attack button when it comes out from behind the waterfall.
Intro - Part 3
X's armor capsule is in this section before the door, under The Bee. It can only be acquired in the revisit. This capsule is part of X's speed route, but not needed for "The Zero Route"
Axl leaves.
Dash and jump with Zero.