All the Riders except the very last one are obtained via Ragnarok Mode, you have to come across them in the levels ; and since most levels have multiple paths, you won't get everyone the first time. You also have to actually take the recruited Riders in your team at least once in Ragnarok mode in order to permanently unlock them in other modes. The main villains of Ragnarok mode are unlocked by completing stage 14 (unlocked after finishing Ragnarok mode once and going back to your completed save) a certain number of times.