I suppose you’re right - I forgot about that one (ffs - I almost always fail The Archive in PUG’s on NORMAL difficulty - the Sentry gets SHREDDED so easily…).
…But there ARE far more PVP-specific ones than Story Mission ones. I think the only ones are those “Play a specific story mission map with additional challenge qualifiers.”, and only a few characters have em (they are always the center one in the lore menu as well, to unlock the character’s audio log).
I don’t count the “unlock character” ones as well, since Gearbox very thoughtfully added a Command Level unlock to all of em, so you do not HAVE to play Story Missions or PVP to unlock them if you don’t want to.
For example, I just finished unlocking Phoebe yesterday even though I’ve never played a single PVP mission (well, I did play ONE to try and get a couple of Thorn’s damn challenge done, but while I got quite a few kills and never stopped jumping, fate conspired to see that none of em were “Volley in the air” kills, so…).
Also, at least you CAN finish the Blight one in PVP (that one mode - Meltdown(?) shouldn’t be too bad for it, as there are a lot of “minion” NPC bots).