For people working on the bestiary (possible spoilers)

[Miyako]

Alright, now that I figured out what actually triggers the entries, I thought I'd share for anyone confused about how it works (still working on this myself because I missed a few my first time). First you need the bestiary potion you can get from the half-open chest you can see from the other side of the river 2 screens up from Minea (it's toward the right side of the screen).

You can go up a screen from the screen with the chest and cross the bridge on the right and go down all the way around to get to the other side. Once you get it, you have to drink it by equipping the item and pressing c to use it (default key, different if you changed it).

A stat is entered for the enemy for every 5 times you kill it (as far as I can tell) if it is a regular enemy. This means you'll have to kill each non-boss enemy 25 times (again, as far as I can tell, haven't tested extensively) to get the achievement. Also keep in mind EXP and gold aren't shown on the overlay, so make sure the entry is complete in your notes.

Thought this might help some people.

[RPG Gamer Man]

Yea..positively get the Bestiary potion or you cannot enter into book the monster information. I second this suggest, and great post btw :)

[desertman2]

Does the data carry over across multiple playthroughs, like in Origin?

[Korzic]

Nope, it resets. I believe Ys II lets you carry over the last boss (bosses are not required for achievements), but besides that, it also resets. Strange, as the prior PC version (Complete) lets you carry monster data across all playthroughs, but oh well.

[Miyako]

yep, gonna have to beat the game again...