being a pokemon fan back in my childhood and a lucid dreamer even longer you've got me imagining how it could be done;

I imagine it would help to keep track of your progress in a dream journal which would act like a pokedex, keeping records each time you dream of which pokemon you have seen and fought, which you have caught and how your progress as a trainer is going. (A dream journal is something you write down your memories from the dreams in to improve recall, in this case you should keep it organized with all the data the pokedex would offer, plus anything else that happens in your adventures and notes on plans for future expeditions.)

Leveling up wouldn't be so mechanical, I'd imagine more like the anime than the game, since progress would be based on how well your dream control can get the pokemon to use certain abilities, you would be training with the pokemon to better know their ins and outs and lead them in battle, victory determined by your ingenuity to overpower and outsmart the opponent. What's great about this is the subconscious naturally has a certain autonomy that would give it the ability to play along with you in this world, from trying to catch pokemon and their attempt to escape the pokeball as a battle of willpower, to the dream character pokemon and trainers having a life of their own to really put up a challenge.

It would definitely take dedication to stabalize such a complex dream, from knowing the make-up of the pokemon world well enough that the subconscious can build a working map, to actually getting it to stay consistant with the world. But if you put enough of the right effort in it is definitely a plausible endeavor, the subconscious is a powerful tool and can surely handle this task if you train it to.