This trophy/achievement is quite a grind, as it requires you to fully research every monster in the game. Ignore the weasel-words "almost every monster", the only one they don’t include is Zorah Magdaros, whose research will be concluded as you advance the story. Otherwise you must full research each monster, who have variable levels of research depending on their rank - monsters with Low Rank variants have six levels, while High Rank exclusive monsters have four levels. You gain Research Points by examining monster tracks, hunting monsters, breaking parts during combat, witnessing turf wars, or by other combat actions, like using traps.
The only monsters who will likely give you much trouble are the Elder Dragons, as until you complete the assignment Thunderous Rumble in the Highlands you can only readily gain Research Points from them during quests to hunt them… which isn’t so bad, as you’ll probably want to hunt them at least several times each to get materials for top-tier armor and weapon crafting. Some Elder Dragons (like Nergigante) are more generous with their tracks, while others (like Kirin) are less generous, perhaps requiring many, many hunts to gain the Research Points necessary. After completing the aforementioned Thunderous Rumble in the Highlands, however, you can start finding Tempered Elder Dragon tracks in static locations throughout various locales; Kushala Daora tracks in the Ancient Forest, Teostra tracks in the Wildspire Waste, Kirin tracks in the Coral Highlands, Vaal Hazak tracks in the Rotten Vale and Nergigante tracks in the Elder’s Recess. While it may be tedious, you can run to these tracks repeatedly, gaining their Research Points, then traveling to another map, filling out your Hunter’s Notes as you go. It’s arguably much quicker than fighting them repeatedly, and it’ll hopefully unlock some useful investigations for you.
A list of all the monsters you must research, and their levels, follows: