This page will detail all the moves Kat has at her disposal. Please keep in mind to expect slight spoilers, as some abilities are not unlocked until you progress in the game.
Your basic jump. You'd think that for a shifter it's not of much use, but since our brains are still used to having an up and a down, it's actually pretty useful for making small adjustments in your positioning. For crossing large gaps, press X, L, R in quick succession: Kat will perform a somersault with only minimal use of gravity energy. The somersault can also be used to climb high ledges.
Your basic attack. Damage is minimal but it comes out very quickly. Kat will perform a variety of combat moves with repeated button presses, including chops. The variety and power of the attacks can be increased by spending gems.
Shifting is done through a single press of the R button. Kat will enter a state of zero-gravity. Use the right analog or Vita's gyro to decide on a direction and press R again to "fall" in that particular direction. The fall will end if you hit an object, and the direction of gravity will be adjusted based on the object you land on. For example, if you shift towards a wall at a slightly off angle, the gravity will realign once you land on the wall so that the wall will be horizontal for Kat. The speed of your fall can be increased by spending gems.
For increased falling speed, you can press and hold down cross (jump button) instead of R. You can also increase your speed mid-fall at any time.
Press L to revert to normal gravity. Becareful when doing this while shifting, as some momentum will be involved depending on the speed of your fall.
Kicking while shifting (either stationary or falling) will cause Kat to perform a flying (dropping) kick towards the center of the screen at the time the kick button was pressed. If an enemy happens to be in Kat's path, Kat will home into the enemy. The degree of homing, as well as the power of the gravity kick can be increased by spending gems.
Adjust a Gravity Kick mid-air
While performing a gravity kick, you can at any time cancel the current maneuver and start another gravity kick anew. This is useful for when you realize Kat is about to miss her target. To adjust your direction of falling, use the gyro or right analog to get the enemy (or other target) in the middle of your screen. Press kick and a new gravity kick will be initiated.
Control Direction of Bouncing
After landing a gravity kick (be it an enemy or an object/wall), Kat will bounce off of anything she has hit. By tilting the left analog, you can control the direction Kat bounces off to. This can be used to stay high in the air after hitting an enemy on the ground (tilt up), or to make targeting the next check point easier in challenges.
Kat is able to carry objects (and people) with her by extending her gravity manipulation to surrounding objects by projecting a so called stasis field which will sweep up any objects in its reach.
To pick up objects deploy Kat's stasis field by pressing the circle button (press and hold to pickup more objects, up to its maximum capacity). Activating the stasis field will make Kat enter shifting mode as well. The maximum amount of objects that can be carried can be increased by upgrading the Stasis Field power.
Any objects that Kat is carrying will stay with her even when you disengage shifting until you throw them by pressing the circle button (or get hit by an enemy). Kat will let go of one object for each press of the button. In case of people or certain mission relevant objects Kat will simply drop them down to the ground. Any other objects will be thrown in the direction you are currently facing, causing massive damage to anything hit by the object. There's no need for perfect aim when throwing objects at enemies; a pink halo appearing around your reticle indicates that the enemy has been targeted and any thrown object will "home" in on it, at least within reason the enemy could still dodge it or the projectile could crash into an obstacle.
By flicking any part of the screen, Kat will initiate an evasive maneuver in the direction of the flick. Kat will be invulnerable to attacks during and for a split second after the maneuver. The number of times this maneuver can be performed in succession can be increased by spending gems. This move can be performed regardless of what Kat is doing: walking, shifting, falling, even during an attack. Although most moves will be cancelled upon performing a dodge, grabbed objects will remain grabbed.
Right after performing an evasive maneuver, press square to have Kat dish out a powerful counter-attack. Note that this can be done even when the enemy was not attacking Kat at the moment of the evasive maneuver.
Holding down the left and right edges of the screen will cause Kat slide over the ground. Steering is done through rotating the Vita (just as you would with a steering wheel). If you let go of one finger while performing a gravity slide, Kat will slow down to a slug's pace. Use this to make turning more comfortable. Jolting the unit while sliding will cause Kat to jump. Jumps can also be accomplished by pressing the cross button: but you will need to use your right index finger to touch the screen in order to free your right thumb. The speed of the slide can be increased by spending gems.
While performing a gravity slide, Kat will dish out a powerful kick when she comes into range of an enemy. This move is at least as powerful as a full-range gravity kick, and useful for breaking shells of enemies, or to clear up enemies that are lined up or packed close together.
This section will detail the three special moves that Kat will learn as she progresses through the story. All special moves can be powered up by spending gems.
Once obtained, can be executed by pressing triangle with the left analog neutral. When executed, Kat will home in on the nearest enemy (or core, in the case of multiple-core nevi) and continue to deal damage until the enemy or core is destroyed, and will then home in on the next nearest target. Powerful, but you have no control over Kat whatsoever, so if she misses she may continue to fly into the wrong direction. As such, best pulled of at point blank range.
Once obtained, can be executed by pressing triangle while tilting the left analog upwards. When executed, Kat will conjure a number of rocks around her, which will home in on any enemies in her line of sight. At higher levels, Kat will fire so many projectiles that you can literally clear an entire wave of enemies by slowly turning with your "camera" after the move has initiated.
Once obtained, can be executed by pressing triangle while tilting the left analog downwards. When executed, Kat will invoke a gravity field around her that will suck in and damage nearby enemies. Although it pales in comparison with the other special moves when it comes to raw fire power, it does have its uses as it can be used to take out nevi with multiple cores that are hard to reach.
This section will detail advanced moves and combinations. Some may appear to be more like exploits; it's hard to tell whether these were all intended by the programmers or not.
When falling in natural gravity, you crash to the ground if you fall from a certain height. You can break the fall by flicking the screen just as you are about to hit the ground.
Bounce of walls
When falling while shifting, you usually "land" on any object that happens to be in your path. There are times (such as in the challenges, but also when you're navigating your way through narrow paths) that you don't want this to happen. To avoid this, simply press R as you are about to hit the wall. You will bounce off the wall and still be in zero-grav mode, allowing you to quickly shift gravity again.
When pressing R while falling, you'll stop, but there's still some momentum involved. If you really want to stop pin-point in mid-air, use the gravity grab (which is assigned to circle in the Japanese version).
Use objects as shields
Grabbed objects will block enemy fire.
Repeat gravity kick
Immediately after landing a gravity kick, cancel the rebound and dish out another kick by pressing L -> R -> square in quick succession. Can be done many times in a row. Be careful though as it also means you're sitting still in a single location, which can make you vulnerable to enemy fire.
While on the ground, press cross and square to perform a drop-kick. More powerful than an ordinary kick, and can reach cores that are higher up.
As stated above, counter-attacks can be used even when the enemy has not attacked. Using this, Kat can perform two high-reaching kicks at will. The first involves evading backwards and then pressing square: Kat will perform a somersault kick Guile-style. The second one involves evading forward (towards the target) and then pressing square: Kat will perform a low flying kick Cammy-style. Both are capable of hitting cores that are out of reach of normal kicks.