Crisis Core's combat system was, in many ways, a predecessor to the active-time battle system of Final Fantasy VII Remake. The game features a fast-paced combat system with a variety of abilities, most of which are still focused around Materia. Materia allows you to cast spells and use techniques, so improving everyone is very important. Unfortunately, it's not really up to you.
Upgrading Materia in Crisis Core
Materia level is controlled by the DMW, the slot machine that spins in the top left corner of the HUD. Whenever two of the three slots land on the same number, the Materia in the corresponding numbered slot receives a single level up. There are six numbers on each wheel, so two lines are likely to come up with the same number pretty often.
Unfortunately, you can't really control which of your Materia gets the upgrade. It's entirely out of your hands, but you can tip the scales in your favor a bit. You'll want to have a lot of high-level Materia on-hand to use Fusions and battle specific enemies. With that in mind, swap your Materia frequently and bring a lot of different tools into combat.
If your Materia feels a bit under-leveled, just take on some easy combat challenges. You need to give the DMW plenty of time to award the outcomes you have in mind. Take on the very first Mission and defeat the enemies very slowly. Statistically, you'll eventually get what you need.
Finally, after unlocking Mission 8-4-4, you can acquire the Moogle Amulet and get the Moogle Power DMW ability. This summon only functions in Chocobo Mode, but if you're lucky enough to get the right spin, all of the Materia you're carrying will be leveled up.
Materia is an important part of Crisis Core's combat system, but you can only hope for the best when upgrading your tools. Take on a lot of easy battles and be ready to grind a bit to get your Materia where you want it to be.
For more on Final Fantasy games and Crisis Core remaster, we at Pro Game Guides recommend What is Final Fantasy VII Ever Crisis? Release date, platforms, games, & more and When is the Final Fantasy VII Remake Intergrade coming to Steam? Answered.