The following is a list of Freya's in game Dragon Magic, as well as other abilities learned from equipment. The list includes the names of these abilities, as well as the MP needed to perform (Dragon Magic); the AP needed to learn (Abilities) and what you can learn them from.
Dragon Magic
Cherry Blossom -:- 46 MP -:- Causes non-elemental damage to all enemies
Dragon Breath -:- 78 MP -:- Reduces HP of all enemies
Dragon's Crest -:- 16 MP -:- Deals physical damage to the enemy
Lancer -:- 10 MP -:- Reduces the enemy’s HP and MP
Luna -:- 12 MP -:- Causes Berserk to all targets
Reis’s Wind -:- 12 MP -:- Casts Regen on entire party
Six Dragons -:- 28 MP -:- Fully restores HP and/or MP/Reduces HP and/or MP to 1/No Change at all!
White Draw -:- 36 MP -:- Restores MP of all party members
Abilities
Ability Up -:- 65 AP -:- Learn from: Diamond Gloves, Diamond Armor, Cachusha, Ribbon, Lapis Lazuli
Accuracy+ -:- 30 AP -:- Learn from: Diamond Helm, Genji Armor, Lapis Lazuli
Add Status -:- 25 AP -:- Learn from: Thunder Gloves, Glass Buckle
Antibody -:- 15 AP -:- Learn from: Bronze Gloves, Mythril Helm, Glass Buckle
Auto-Float -:- 20 AP -:- Learn from: Venetia Shield, Feather Boots
Auto-Haste -:- 75 AP -:- Learn from: Running Shoes
Auto-Life -:- 125 AP -:- Learn from: Rebirth Ring
Auto-Potion -:- 30 AP -:- Learn from: Running Shoes, Gold Choker, Extension
Auto-Reflect -:- 95 AP -:- Learn from: Reflect Ring
Auto-Regen -:- 25 AP -:- Learn from: Carabini Mail, Angel Earrings, Maiden Prayer
Beast Killer -:- 25 AP -:- Learn from: Platina Armor, Black Belt, Moonstone
Bird Killer -:- 30 AP -:- Learn from: Bronze Armor, Chain Mail, Yellow Scarf
Body Temp -:- 20 AP -:- Learn from: Genji Armor, Madain’s Ring, Fairy Earrings, Diamond
Bright Eyes -:- 10 AP -:- Learn from: Iron Helm, Cachusha
Bug Killer -:- 25 AP -:- Learn from: Mythril Gloves, Bronze Helm
Chemist -:- 35 AP -:- Learn from: Grand Armor, Madain’s Ring, Barette
Cherry Blossom -:- 40 AP -:- Learn from: Obelisk, Kain’s Lance
Clear Headed -:- 35 AP -:- Learn from: Lamia’s Tiara, Gold Helm, Magician Shoes
Counter -:- 85 AP -:- Learn from: Venetia Shield, Anklet, Power Belt
Cover 30 Gauntlets, Linen Cuirass, Mythril Armor
Devil Killer -:- 30 AP -:- Learn from: Thunder Gloves, Cross Helm
Distract -:- 25 AP -:- Learn from: Shield Armor, Reflect Ring, Diamond
Dragon Breath -:- 205 AP -:- Learn from: Dragon’s Hair
Dragon Crest -:- 45 AP -:- Learn from: Holy Lance, Kain’s Lance
Dragon Killer -:- 70 AP -:- Learn from: Javelin, Barbut
Eye 4 Eye -:- 35 AP -:- Learn from: Kaiser Helm, Rubber Suit
Gamble Defense -:- 20 AP -:- Learn from: Barette
High Jump -:- 75 AP -:- Learn from: Dragon Mail
High Tide -:- 20 AP -:- Learn from: Partisan, Genji Gloves, Grand Helm, Minerva’s Plate, Demon’s Mail, Sapphire
HP+10% -:- 30 AP -:- Learn from: Chain Mail, Germinas Boots, Aquamarine
HP+20% -:- 75 AP -:- Learn from: Defense Gloves, Genji Helmet, Black Belt
Initiative -:- 95 AP -:- Learn from: Obelisk, Battle Boots
Insomniac -:- 30 AP -:- Learn from: Mythril Helm, Diamond Helm, Coral Ring
Jelly -:- 30 AP -:- Learn from: Dragon Wrist, Diamond Gloves, Mythril Armor
Lancer -:- 20 AP -:- Learn from: Partisan, Dragon Wrist, Coral Ring
Level Up -:- 40 AP -:- Learn from: Iron Helm, Rosetta Ring, Fairy Earrings, Pearl Rouge, Extension
Locomotion -:- 25 AP -:- Learn from: Plate Mail, Anklet
Long Reach -:- 210 AP -:- Learn from: Protect Ring
Luna -:- 30 AP -:- Learn from: Trident
Man Eater -:- 20 AP -:- Learn from: Mythril Gloves, Coral Ring
MP+10% -:- 35 AP -:- Learn from: Magician Shoes, Extension, Emerald
MP Attack -:- 20 AP -:- Learn from: Cross Helm, Battle Boots, Power Belt
Reis’s Wind -:- 25 AP -:- Learn from: Mythril Spear, Holy Lance, Gold Helm, Angel Earrings
Restore HP -:- 85 AP -:- Platinum Helm, Minerva’s Plate, Grand Armor, Promist Ring
Six Dragons -:- 25 AP -:- Learn from: Heavy Lance
Stone Killer -:- 20 AP -:- Learn from: Platinum Helm, Gold Armor
Undead Killer -:- 20 AP -:- Learn from: Silver Gloves, Plate Mail
White Draw -:- 65 AP -:- Learn from: Ice Lance, Kain’s Lance, Emerald