Totally possible! hahah
I did a lot of soloing during the beta, since I didn't have any friends :( haha
I was a Lancer, rank 13+ and my PL was a bit higher (cause I did a lot of crafting). With decent VIT, I was able to solo most, if not all, of the missions that require "finding" a disguised enemy - like the ones with Firestarter Imps.
What I would do, if you're really not sure, is figure it out. There's nothing wrong with failing a leve as far as I know, except the wait period to do something else. Start up a few that sound not too horrible and see what you can do.
On a side note, my strategy for the Imps mission was usually:
1) Run into group, stab one enemy.
2) If they turn into Imps, run away until you leave combat, then buff yourself, if applicable (I did this because I kept wasting Ferocity or Bloodbath or something on the first hit, and if they turn into the Imps, you lose that... Then the Imps nuke you!)
4) If they don't turn into the enemies, you'll probably wanna run away. THAT'S when you'll probably die... hahah