Complete the specified requirement to unlock the corresponding rider when they are encountered in Ragnarox mode (except W/Double CAX). Multiple attempts may be required and with the exception of W/Double CAX you have to take the recruited rider in your team at least once in Ragnarok mode to permanently unlock them in other modes.
Unlock Scissors: Complete Stage 14 once.
Unlock Ouja: Complete Stage 14 two times.
Unlock Nega Den-O: Complete Stage 14 three times.
Unlock Ryuga: Complete Stage 14 four times.
Unlock Dark Kabuto: Complete Stage 14 five times.
Unlock Odin: Complete Stage 14 six times.
Unlock Garren: Unlock ALL other riders except himself and W/Double CAX. (you may need to complete Stage 14 again).
Unlock W/Double CAX: When you have unlocked Garren choose Arcade mode and select the last empty space. Then press Square for a random character and complete Arcade mode as W/Double CAX.