I found you can make a skill chain with Ifrit's Double Punch. It falls into the category of the following Weapon Skills:
One-Inch Punch
Keen Edge
Nightmare Scythe
Penta Thrust
Skewer
Star Burst
Sun Burst
Blade: Ei
Black Halo
Tachi: Kasha
You can substitute one of these Weapon Skills for Double Punch (i.e. Red Lotus Blade > Double Punch = Gravitation).
Enjoy :)