Digimon Story: Cyber Sleuth - Hacker's Memory

To check your progress on this trophy open the Field Guide in your pause menu () and look at the top right corner. The trophy will pop when the Digimon Registered reads 300 and to have a Digimon be registered and increase your total you must have actually OWNED said Digimon at some point.
To compare it to Pokemon's Pokedex:
Digimon Encountered = Pokemon Seen
Digimon Registered = Pokemon Caught
Since Digimon don't have one linear evolution tree like Pokemon do this trophy is much easier than it seems.

For example Koromon can Digivolve into 6 different Rookie level Digimon so we'll follow the Agumon route from the anime.
Koromon > Agumon > Greymon > MetalGreymon > WarGreymon > Omnimon
as you can see this Digivolution tree has a total of 6 forms from Koromon to Omnimon so every time you get a new Digimon for the first time it counts as one.
Let's say I used the Digimon Black Market and bought my first Greymon and then I immediately went to the DigiLab and used the DigiConvert option to make my first Koromon.
If I Digivolved Koromon to Agumon, then that same Agumon to Greymon, then that same Greymon to MetalGreymon that would be 4 new registries HOWEVER because I bought that Greymon from the black market it doesn't count as a new registry and therefore I'm only given credit for 3.

You can Digivolve your lower levels to their Mega forms, then De-Digivolve those Mega forms to an unregistered Ultimate form provided you have discovered (encountered) that Digimon.
Any Digimon you can't De-Digivolve to will be a silhouette with ??? for a name and will say "De-Digivolution Not Possible..."
Digimon you can De-Digivolve into will just be a faded image with a proper name and will say "De-Digivolution Possible!"

The trophy will pop when you open your guide when there's 300 registered Digimon.