The Mortys you find in Campaign will depend on the number of badges you've earned - so for example if you have 35 badges then anytime you into a dimension, you will find Mortys available for players who have 1,2, 3...up to 35 badges (you don't stop seeing Mortys from lower badge tiers just because you gain more badges along the way).
That being said, you will have to jump around until you find the Mortys you're looking for. The algorithm for entering dimensions is randomized, so you don't have the option to pick like in Multiplayer.