when you start super training you have access to level 1 mission (level 1 defense is geodude)
when you clear them all with any pokemon you unlock level 2 missions (level 2 defense is graveller)
when you clear all level 2 missions with any pokemon you unlock level 3 missions (level 3 defense is golem)
when your pokemon has maximum evs (the yellow meter on the right is full) and you complete a level 3 mission with them you unlock secret missions which reward evolutionary stones and other such things
any pokemon can do missions 1-3 once they're unlocked so unlock them and then only play those ones
also you can't raise every stat, every pokemon can only have 510 evs (the points you're earning) total, which is enough to max out two stats of your choosing and then put a tiny bit more into a third
tl;dr find a pokemon you dont really care to train, play through every mission with it until you have all the level 3 missions complete, then play the level 3 spatk mission with your ralts until it's spatk (or atk if you want it to become a gallade) is maxed out, then do it again with another stat (recommend speed if you just want to blow everything up)