Are DLC trophies missable?

[Umdytr]

I recently completed Shenmue I&II, thinking of starting III when I grab another month of Plus Extra.

 

Since the DLC packs aren't included there I would probably buy them after playing through the main game, which is why I'm interested to know if their content becomes missable as you progress through the story. That'd force me to do a whole second playthrough, in which case I'd be better off buying the DLCs and working on those trophies from the start.

[HuntingFever]

Some are, some aren't: https://www.playstationtrophies.org/game/shenmue-iii/guide/