When you are leveling up your Sync Pair, at the final level cap stage, it will ask you for a material that you may not have seen so far in the entire game. These are called Gym Notes.
Gym Notes in this game are used to limit break the final level of every single Sync Pair.
There are currently three ways of obtaining Gym Notes.
Method 1: Drop from Supercourses
Gym Notes are dropped from the daily Supercourse rotation, only during Role-Specific Supercourses (Striker, Support or Tech-Supercourses). Gym Notes will not drop from Level-Up and Coin-courses. Gym Notes only drop on Very Hard difficulty. Normal and Hard difficulties don't drop them. The drop rate for the Gym Notes here are 50%.
Method 2: Farming Co-op Battles
For those that want to grind, and want their Gym Notes immediately rather than waiting for daily Supercourses to rotate around, you might wanna do Main Story Co-Op. There is 10% drop chance of getting a Gym Note. It is recomended to do Brock Hard, as everyone spams it, so it is definitely the most attractive / fastest approach.
Method 3: Item Exchange
Finally, the 3rd method is to exchange 100 Skill Capsules for one Gym Note. This is not recommended as every single passive skill in this game costs 10 Skill Capsules. One will need close to 1000 Skill Capsules to unlock every single Passive skill in the game, so it is recommended to stock up on those.
Personal Note from the Author
P.S. Some advice on your first time: Supercourses very hard. If you are facing bulky enemies, it might be easier for you to take out their side allies as they are the main damage dealers. The enemy’s bulky support unit might hurt with their sync move but outside of that they should be harmless. After a few max level Sync Pairs rest of the Supercourses should be easy. Also I've never personally done any Co-op farming, and I've been doing Supercourses daily. Today, after playing the game for about a month with the limited-release version, I have 50+ Gym Notes collecting dust. Please do not rush Gym Note Grinding and burn yourself out, you will with time have more than plenty. So enjoy the game! - Sincerely Emma.