As for collections, I have two for the PS2, Atari Anthology and Sonic Mega Collection Plus. The Atari one I’d have to double check since I don’t remember, but the Sonic one has at least unlockable (often non-Sonic-related) games by hidden conditions, so maybe that’d count? Though the condition is pretty simple, open a certain game or games an X number of times.

Also just checked Dissidia 012 and Crisis Core. Dissidia 012 has an achievement system, Crisis Core doesn’t seem to have one.

For Dissidia 012, open the customizations menu with triangle with the character you want to check character-specific achievements, go to the right and open the first entry, Accomplishments.