Another obligatory grind trophy? Digimon you spoil us...
The max rank is 20 and by the endgame you should be between 10 and 15 depending on how many miscellaneous cases you've done on top of the main story ones.
There's only one way to grind your levels out, which is by completing cases, but there are two ways to approach it: grind them on the first playthrough in post-game or start NG+.
Personally I would go for the NG+ approach because the main story cases give out far more EXP and variety than the optioonal cases do; just remember that you should get the Memory Spinner trophy before starting NG+ as the memories you collect do not transfer over!