Tail Blade (Z, on ground) - basic melee attack. Does lowish damage with close to 360' coverage; knocks back. Due to how this game works, you'll probably mostly only use this to deal damage over enemy blindspots/safespots e.g. directly above a stationary cannon. Later receives an upgrade to send a fairly mid-ranged sword beam forwards.
Normal Shot (C, on ground) - basic ranged attack. Machinegun. Very low damage, adds up. Later receives an upgrade to gain a piercing effect.
Air Raid (Z+any direction, midair) - basic melee attack. Low damage, but has a very quick 'dash' effect to the direction of input. 8-way dash tool, including for double jumps. Longer reach but longer cooldown delay than Burst. Later receives a damage upgrade.
Burst (C, midair) - basic ranged attack. Shotgun. Very low damage, adds up. Later receives an upgrade to gain a piercing effect. Very powerful against crowds of tiny enemies. Slight upward recoil, can be used as a double jump tool, though not to the same extent as Air Raid.
Gatling (V, on ground) - straightforward ranged attack. Does fair damage, pierces all in a line, knocks back, short cooldown. Is ground-only, has a narrow range and fair delay, so be careful when using on bosses. Will likely be largely supplanted by Arm Cannon later on, but gains an upgrade very late.
Chase Missile (Up+V, on ground (midair)) - creates homing projectiles. Very easy to use, fire-and-forget, fairly high damage too, but has a somewhat long delay. Later receives an upgrade to Super Chase Missile, becoming usable midair and becoming overall much more user-friendly, and then gains even more upgrades. Will probably be one of your most used attacks vs mooks and bosses both.
Satellite Beam (Down+V, ground/air) - control a targeting reticle for a short time and send a beam down on that position. Long cooldown, low damage each hit, lots of hits. Particularly convenient due to its vertical reach, but suffers against fast-moving enemies/bosses. Gains an upgrade later.
Ignis (S, ground/air) - spawns a bit that stops and scatters piercing bullets in a spin. Low damage, but can build up if the enemy is right on top of the bit and thus all of its bullets. Has very low delay and thus can be used as a source of cheap DPS whenever it's off cooldown. Gains an upgrade to self-destruct for surprisingly okay damage, and another to boost firepower.
Arm Cannon (Up+S, ground/air) - powerful ranged attack. Does fair damage in a deceptively large AoE. Easily busts through 'armored' enemies. Short cooldown too. Can be used as a steady source of DPS against bosses.
Laser Cutter (Down+S, ground/air) - spawns a rotating laser blade at around the same spot as the Ignis bit to rapidly do low damage in its AoE. Very short cooldown. Best vs small mooks or slow/immobile enemies, or for denying destructible projectiles. Has very low delay, can also be used as a source of cheap DPS whenever it's off cooldown. Gains an upgrade to create a second protective Cutter around Beth for projectile denial, and another to increase damage.
Concentrate (D, ground/air) - creates a high-damaging explosion some ways in front of Beth. Has high damage and wide range, but a blindspot right in front of her. The upgraded version is probably one of the better DPS sources out there. The comparatively short delay helps too.
Eclair (Down+D, ground/air) - creates a lightning laser blade and slices forward. Fairly quick to deploy, highest damage out of all 'basic' special attacks, and the longest cooldown. Try to get as many of these off in a boss fight.
Meteodrive (A, ground) - super move #1. Standard 'damage everything in the vicinity' move. Can be used to wipe out clusters of enemies, as a quick-and-dirty damage source when fighting a boss, or for the short invincibility period during the move.
Artemis (Down+A, ground) - super move #2. Spawns a huge bit that provides fire support in basically every way. Excellent DPS booster. A later upgrade also adds a secondary machinegun to your C. Seemingly does more damage than the other two supermoves, but over a longer time period. Also, the gigantic bit can get in the way of dodging enemy bullets by obscuring sight.
Detonation (Up+A, ground/air) - super move #3. Giant laser beam. Has a significantly narrower range than Meteodrive, but seems to do slightly more damage if all hits connect.