Leveling Up:
* 1: Gust
* 4: Tackle
* 7: Silver Wind
* 10: Quick Attack
* 13: Razor Leaf
* 16: Stun Spore
* 19: Sunny Day
* 22: Bug Buzz
* 25: Air Slash
* 28: Hidden Power
* 31: Aerial Ace
* 34: Solar Beam
* 37: Quiver Dance
* 40: Baton Pass
* 43: Hurricane
* 46: Tailwind
TMs:
* 01: Quick Attack
* 04: Calm Mind
* 06: Toxic
* 10: Hidden Power
* 15: Hyper Beam
* 16: Light Screen
* 17: Protect
* 20: Substitute
* 21: Dizzy Punch
* 24: Thunderbolt
* 25: Thunder
* 27: Return
* 29: Psychic
* 30: Shadow Ball
* 31: Brick Break
* 32: Double Team
* 39: Facade
* 40: Aerial Ace
* 42: Facade
* 44: Rest
* 45: Attract
* 47: Sunny Day
* 48: Skill Swap
* 50: Overheat
* 53: Energy Ball
Breeding:
* Fairy Wind: Learned from Spritzee, Swirlix, Azurill, and others.
* U-turn: Learned from Azurill, Bibarel, and others.
* Light Screen: Learned from Azurill, Luvdisc, and others.
* Reflect: Learned from Azurill, Luvdisc, and others.
* Wish: Learned from Azurill, Luvdisc, and others.
* Defog: Learned from Azurill, Luvdisc, and others.
* Healing Wish: Learned from Azurill, Luvdisc, and others.
* Tailwind: Learned from Azurill, Luvdisc, and others.
* Safeguard: Learned from Azurill, Luvdisc, and others.
* Roost: Learned from Azurill, Luvdisc, and others.
* Moonlight: Learned from Azurill, Luvdisc, and others.
* Morning Sun: Learned from Azurill, Luvdisc, and others.
* Synthesis: Learned from Azurill, Luvdisc, and others.
* Giga Drain: Learned from Azurill, Luvdisc, and others.
* Calm Mind: Learned from Azurill, Luvdisc, and others.
* Nature Power: Learned from Azurill, Luvdisc, and others.
* Hidden Power: Learned from Azurill, Luvdisc, and others.
* Signal Beam: Learned from Azurill, Luvdisc, and others.
* Round: Learned from Azurill, Luvdisc, and others.
* Thunder Wave: Learned from Azurill, Luvdisc, and others.
* Thunderbolt: Learned from Azurill, Luvdisc, and others.
* Thunder: Learned from Azurill, Luvdisc, and others.
* Charm: Learned from Azurill, Luvdisc, and others.
* Attract: Learned from Azurill, Luvdisc, and others.
* Belly Drum: Learned from Azurill, Luvdisc, and others.
* Substitute: Learned from Azurill, Luvdisc, and others.
* Will-O-Wisp: Learned from Azurill, Luvdisc, and others.
* Protect: Learned from Azurill, Luvdisc, and others.
* Detect: Learned from Azurill, Luvdisc, and others.
* Endure: Learned from Azurill, Luvdisc, and others.
* Quick Attack: Learned from Azurill, Luvdisc, and others.
* Double Team: Learned from Azurill, Luvdisc, and others.
* Amnesia: Learned from Azurill, Luvdisc, and others.
* Agility: Learned from Azurill, Luvdisc, and others.
* Soft-Boiled: Learned from Azurill, Luvdisc, and others.
* Minimize: Learned from Azurill, Luvdisc, and others.
* Transform: Learned from Azurill, Luvdisc, and others.
* Swagger: Learned from Azurill, Luvdisc, and others.
* Substitute: Learned from Azurill, Luvdisc, and others.
* Copycat: Learned from Azurill, Luvdisc, and others.
* Encore: Learned from Azurill, Luvdisc, and others.
* Fake Tears: Learned from Azurill, Luvdisc, and others.
* Spite: Learned from Azurill, Luvdisc, and others.
* Trick: Learned from Azurill, Luvdisc, and others.
* Grudge: Learned from Azurill, Luvdisc, and others.
* Heal Bell: Learned from Azurill, Luvdisc, and others.
* Reflect: Learned from Azurill, Luvdisc, and others.
* Light Screen: Learned from Azurill, Luvdisc, and others.
* Psych Up: Learned from Azurill, Luvdisc, and others.
* Cosmic Power: Learned from Azurill, Luvdisc, and others.
* Magic Coat: Learned from Azurill, Luvdisc, and others.
* Sweet Scent: Learned from Azurill, Luvdisc, and others.
* Teeter Dance: Learned from Azurill, Luvdisc, and others.
* Covet: Learned from Azurill, Luvdisc, and others.
* Thief: Learned from Azurill, Luvdisc, and others.
* Snatch: Learned from Azurill, Luvdisc, and others.
* Destiny Bond: Learned from Azurill, Luvdisc, and others.
* Perish Song: Learned from Azurill, Luvdisc, and others.
* Grudge: Learned from Azurill, Luvdisc, and others.
* Spite: Learned from Azurill, Luvdisc, and others.
* Last Resort: Learned from Azurill, Luvdisc, and others.
* Follow Me: Learned from Azurill, Luvdisc, and others.
* Uproar: Learned from Azurill, Luvdisc, and others.
* Captivate: Learned from Azurill, Luvdisc, and others.
* Charm: Learned from Azurill, Luvdisc, and others.
* Captivate: Learned from Azurill, Luvdisc, and others.
Move Tutor:
* Aerial Ace: Learned from Move Tutor.
* Baton Pass: Learned from Move Tutor.
* Bounce: Learned from Move Tutor.
* Fury Attack: Learned from Move Tutor.
* Heat Wave: Learned from Move Tutor.
* Iron Head: Learned from Move Tutor.
* Quick Attack: Learned from Move Tutor.
* Tailwind: Learned from Move Tutor.
* U-turn: Learned from Move Tutor.
Note: Some moves can only be learned through breeding, and some require a specific Pokémon as the parent. It is also important to remember that some moves may not be available in Emerald due to generation differences.