Unit data is unlocked usually by destroying various enemy types, even friendly ones. You shouldn't expect this to unlock until you're nearly done with the third playthrough (if you've been doing most of the side quests). You'll receive a notification in the bottom right telling you when unit data has been unlocked, and can check your total in the pause menu.
The standard enemies (stubby, short biped, medium biped, goliath, small flyer, medium flyer) appear in every region of the game with slight appearance variations. Each variation counts as its own unit data whether it be a weapon change for the unit or merely a cosmetic change.
If peaceful enemy units can be killed, doing so will usually grant you unit data (don't worry, they'll either regenerate or the game will reload your save).
Some unit data is gained on units (especially peaceful ones) by completing side quests. You will encounter some unique enemies only by taking sidequests.
Lots of new enemy types show up in the third playthrough, even in areas where you might not have any reason to go (ie, a dinosaur-type unit in the waterfall/river area of the forest).
There is a side quest that shows up in the third playthrough in the castle that requires 95% unit data unlocked to complete, but you don't need to do this. It is an incremental quest, and is unnecessary for any other achievements.
If you don't want to do it legit, you can fully complete three playthroughs and then unlock the trophy in the trophy shop run by the strange girl in the resistance camp.