The following secret moves can be executed.

Temjin
Tokyo Sword Rifle: Jump and press Up + Left Fire + Right Fire.
Long Bomb: Dash backwards and press Left Fire.

Dorkas
Mega Spin Hammer: Press Right Turn + Left Fire + Right Fire.

Fei-Yen
Super Heart: Be in hyper mode and press Left Fire + Right Fire while standing still.

Belgdor
Blue Missile: Press Guard + Left Fire + Right Fire.

Viper II
SLC Dive: Jump and press Up + Left Fire + Right Fire.

Bal-Bas-Bow
Super Bit: Jump and press Left Fire + Right Fire.
Ring Bit: Dash backwards and press Left Fire + Right Fire.

Arpharmd
Mini Bomb: Dash left or right and press Left Fire.
Rushing Attack: Press Guard + Left Fire + Right Fire.

VR Radien
Bouncy Bomb: Dash backwards and press Left Fire.
Time Bomb(?): Dash backwards and hit the corner of a building.
4 Way Standing: Press Guard + Left Fire + Right Fire.