Introduced in Infinity 2.0 are skill trees, which can unlock new abilities or increase a character's power. To access the skill tree, simply press the menu/start button and select skill tree. From there you can see your character's unlocked and purchasable skills. To unlock a skill to purchase, you must purchase a skill connected to it. To purchase a skill, you need skill points (1-6 depending on the skill). You get skill points by leveling up, with higher levels granting more skill points.
Simply purchase 30 of these upgrades across all characters tied to your Infinity profile and the achievement will be yours. If you are going for the level 20 achievements, this will come naturally as a single level 20 character will have purchased enough upgrades to almost get the achievement by themselves.
Alternatively, if you want this fast, if you've got a leveled character from the first Infinity game, they can be used here and will retain their level and thus can have a large pool of skill points to immediately spend. Also to note with this route, if you had a level 15 character from the 1st game, they actually kept accumulating exp. even after hitting the cap. So, they will initially spawn at level 15, but will readjust to the appropriate level upon earning any experience, potentially getting even as high as the new level cap of 20.