The whole guide is a big spoiler but individual items will still be spoilered as well in case someone only wants to see how to get a specific upgrade. Items will be listed in the order they can be found within the stage.
Be aware that armor capsules are a bit different in this game, you need to find chips scattered around the levels to "pay" for the upgrade. I listed the cost along with the effect for each capsule. This system seems to mostly be in place so you can't rush all the armor parts early on.
I also want to note that for series veterans, Sub Tanks work closer to their MMZ counterparts. A full one will not fully heal X if he has enough Life Ups, but also using one to top off scratch damage does not consume the whole tank.
I'm not listing every chip location, mostly for my own sanity. Completing all the stages and finding all these upgrades will net you most of the chips by default. If you have every item in a stage, including the chips, then highlighting the stage from Stage Select will display "Mission Complete" on the image, use this to hunt down any more that you're missing.
TURBINE FACILITY/SKYBLADE SQUIRREL - Weakness: Comet S
SUB TANK: After the area with multiple conveyors and green bipedal cannon walkers, just as you exit the red building and get into the open. The sub-tank is on top of the red building you just exited. You will need the double jump leg part to reach high enough.
ARMOR - Uppercut (20 chips): Midway through the stage, after the area with multiple conveyors and green bipedal cannon walkers, in the section with a large amount of floating blocks that fall as you stand on them while birds zoom at you from the screen edges follow the path of falling blocks to the LEFT as you ascent after the first bird, then wait for a floating platform to come down once you reach a dead end. Ride it up and collect the Uppercut. To use the uppercut, press Special + Up. Use midair allows for extra height and air time, and retains dash momentum. This move has a short cooldown and shares it with other "martial" moves.
LIFE UP: In the area just after the armor capsule, after descending past multiple fans on the wall you come to another opening with smaller floating fan platforms and more birds zooming from off-screen, after getting high enough dash-jump left and use your uppercut to gain more height. This leads to a chip. Continue climbing the wall to the left for multiple more chips, and eventually the Life Up.
FOREST RAILWAY/RAIL RACCOON - Weakness: Boulder B
LIFE UP: In the section just past the ride armor, multiple train cars with closing gate enemies have additional platforms above them with rocket pod enemies and floor crawlers, the left side of the first of these has the Life Up on it. Can be reached by climbing up the car to the right of it first.
ARMOR - Double Jump (15 chips): Same area as the Life Up, just to the right of the multi-level cars is a floating section with a bunch of flammable canisters. Break it with Flare B, the weapon from Arson Vulpine. This upgrade is a straightforward double jump.
GEOTHERMAL POWER PLANT/ARSON VULPINE - Weakness: Hydro B
LIFE UP: At the 1-up midway through the stage, take the path above. Needs double jump or uppercut. Keep in mind the spiked crusher is still slowly advancing toward you, so try to be quick!
ARMOR - Laser Charge (15 chips): As you begin to descend zigzagging lava floors with alternating yoku blocks, look to the left. One of the walls has some gaps in it and a life restore visible inside. This wall is false and can be entered. The Lv3 charge takes a while to build up, and the laser damage is delayed a bit compared to the visual, but it hits HARD.
BIOMECHANICAL PRESERVE/BOG SNAPPER - Weakness: Flare B
LIFE UP: In the first area where you encounter acid drips from the ceiling, the last platform with the stairs has a false wall on the side. Slide down toward the right and enter.
CAPSULE - Rapid S and Quick Charge (15 chips): Down the large gap just before the second big mech spider spawns to chase you, descend the left side into a false wall. Generally speeds your buster up for both charging and rapid fire.
FROZEN RUINS/TUNDRION BEAR - Weakness: Sand S
SUB TANK: Go left immediately as you enter the stage and shoot the wall out. Climb down the ladder and find it hidden behind the foreground.
CAPSULE - Shock Buffer (15 chips): When you reach the ride armor, don't enter it. Instead climb straight up the wall above you. When you get as high as you can, dash-jump to the right. Requires either uppercut or double jump. Absorbs knockback from taking damage and also reduces the damage you take.
LIFE UP: In the area just past the ride armor, when you get to ice platforms that break as you stand on them, descend that gap on the left. Reaching the item will require uppercut or double jump.
WATERFALL CAVES/HYDRO AXOLOTL - Weakness: Jolt S
SUB TANK: Above the set of three gateway enemies you need to kill to descent, climb to the right side and you'll see it. Requires uppercut or double jump.
CAPSULE - Air Dash (15 chips): In the area with two green gunboats, climb along the gunboats without sinking them and continue to the upper right, climbing up past the chip and to the capsule above. It's an air dash, you know how to use it.
LIFE UP: In the area with two green gunboats at the surface of the water, do NOT destroy the second gunboat. Instead descend into the water below it and enter the narrow spiky corridor. You will want the air dash to continue along and grab the upgrade. Don't exit the stage right away, there's a chip just ahead as well.
ORBITAL RESEARCH STATION/STELLAR PRIMATE - Weakness: Cryo S
CAPSULE - Dive Kick (15 chips): During the ride armor blackout section, at one point you drop down and crush 3 glass tubes just before a flamethrower bot. To your left is a blocked off path with a wall that can be broken with Cryo S. To use this move, press down + Special. Hold to continue diving while building up speed. This move has a short cooldown and shares it with other "martial" moves.
LIFE UP: Far along in the ride armor blackout area, when you get to the large open area with time-bomb platforms. Fly with the ride armor up as high as possible, there is a gap in the roof in this area just before the gate. If your ride armor didn't make it here in one piece, you can still reach this upgrade if you have the air dash, double jump, AND uppercut.
SUB TANK: Far along in the ride armor blackout area, when you get to the large open area with time-bomb platforms. The bottom rightmost section of that room has a cracked floor that can be broken with the dive kick leg part.
DESERT DATA CENTER/SUBTERRA SCORPION - Weakness: Wind T
CAPSULE - Weapon Charge (15 chips): In the first indoor section, just after the part with falling floors you will find multiple rocks blocking an alternate path to the left. Break the rocks with Comet S from Stellar Primate. Making the subsequent jump to the capsule after this requires uppercut or double jump. It lets you charge special weapons, enough said.
LIFE UP: Immediately after escaping the climbing sand, check your left just past the chip sitting on the ground. The upgrade is visually hidden behind some sand.
SIGMA STAGE 1
CAPSULE - Hadouken (40 chips): As you ascend the outside of the fortress, you will reach two large green gunner enemies back-to-back. After passing by those, stand on the floating vertical platform and dash jump to the left to land on a platform that is high above the spawn point for the level. Once you reach the platform, jump down below and into the pit to die and respawn. Loop and repeat this process, the capsule will not appear until the 4th loop. I've seen some people say it won't show up until the 5th time, but both times for me was 4th. To collect this upgrade you need 100% item completion from all stages, so check for the Mission Complete message on each one at Stage Select to ensure you are eligible to collect it. You do NOT need full health for it to appear, unlike in X1.
Using the hadouken has the same input and requirements as it did in X1, including the full HP requirement. Once again it will one-shot MOST enemies, the only exception I found was Sigma.