Most were transfer from SIN data (but obviously this time doing "Fairy Summoning" combo isn't as easy -__-). If under ORDER saids "fire", "water", "earth"..etc., it means it can be any magic of that element.
Since the list is too long, I've divided it into 3 parts.

**Note: All combo with "Fairy Summoning" happens only obtaining demon rumors.

FIRE - HEAT | MULTI - PHYSICAL | SPECIAL

FIRE (AGI)
Name	Target	Order
Explosive Flame	Enemy Single	Fire --> Fire
Tower Infernal	Enemy Single	Water --> Earth --> Fire
l'oiseau de feu	Enemy All	Fire --> Earth --> Maharagi
Mega Flares	Enemy All	Fire --> Earth --> Maharagion
Metal Down	Enemy All	Fire --> Earth --> Maharagidan
Mega Raw Fire	Enemy All	Fire --> Multi--> Deadly Bang
Salamander	Enemy All	Dainamic Agiraon --> FairySummoning
WATER (AQUA)
Name	Target	Order
Evil Cloud Rainfall	Enemy Single	Water --> Water
Hydro Robest	Enemy Single	Earth --> Wind --> Water
Speed Water Claw	Enemy All	Water --> Wind --> MahaAqua
Titan Wave	Enemy All	Water --> Wind --> MahaAques
Bang Slash	Enemy All	Water --> Wind --> MahaAquadan
MaleStorm	Enemy All	Water --> Multi--> Aqualidat
Undine	Enemy All	Wonderful Aques --> FairySummoning
WIND (GARU)
Name	Target	Order
Dragon Flying	Enemy Single	Wind --> Wind
Kamaitachi	Enemy Single	Fire --> Water --> Wind
Airless Wave	Enemy All	Wind --> Water --> MahaGaru
Giga Cycle	Enemy All	Wind --> Water --> MahaGaru
Maxin Best	Enemy All	Wind --> Water --> MahaGarudan
Storm Nightmare	Enemy All	Wind --> Multi--> Twinkle Nebula
Silf	Enemy All	Dangerous Garura --> FairySummoning
EARTH (MAGNA)
Name	Target	Order
Sharp Rock	Enemy Single	Earth --> Earth
Stone Lance	Enemy Single	Water --> Fire--> Earth
Last Spark	Enemy All	Earth --> Fire --> Magna
Click Fang	Enemy All	Earth --> Fire --> Magnus
Last Quake	Enemy All	Earth --> Fire --> Magudan
Hell Desert	Enemy All	Earth --> Multi--> Land's Warth
Norm	Enemy All	Great Magnus--> FairySummoning
ICE (BUFU)
Name	Target	Order
Ice Blast	Enemy All + Freeze	Ice --> Ice
Ice Crash	Enemy All + E.Shock	Ice --> Multi --> Dimond Dust
Giga Frost	Enemy All	Atomic Bufura--> FairySummoning
THUNDER (GIO)
Name	Target	Order
Thunder Blast	Enemy All + E.Shock	Thunder --> Thunder
Thunder Crash	Enemy All + E.Shock	Thunder --> Multi --> Thunder Purify
Takemi Katsuchi	Enemy All	Hyper Gionga--> FairySummoning
HEAT
Name	Target	Order
Heat Blast	Enemy All	Heat --> Heat
Heat Crush	Enemy All	Heat --> Multi --> Nuclear Missle
Hinokakuchi	Enemy All	Ultra Flara --> FairySummoning

FIRE - HEAT | MULTI - PHYSICAL | SPECIAL