In order to obtain the trophy, you have to play through every base game character's story. The ones that are added through DLCs don't count.
Every character's story is made of mixed chapters, some are only narrative and some are fights.
Some of them are not immediately available and you have to unlock them by playing another character:
Azwel story is unlocked by completing Groh's story.
Siegfried is unlocked by completing Nightmare's story
Cervantes is unlocked by completing Ivy's story.
Note that Zasalamel has only narrative chapters.
All character's chapters are fairly easy to beat, you just need some patience.