Heads I Win, Tails You Lose: Sister Mary has an extremely forgiving Personal Story, which is won by two people in the game being Blessed, and is lost by her being cursed (which is less likely to happen to her, because she starts the game as Blessed). If she succeeds, she gets Blessed again if she's not already and gets total immunity to curses. If she somehow loses, she outright No Sells the curse and becomes blessed instead.
Luck-Based Mission: The goal of his personal story is to get a Dreamlands trophy, with the fail condition being if the doom track hits 5. The problem is that opening gates typically advance the doom track, which means that absent somebody starting with the Control Gate spell or fortunately-timed monster surges, Pete's only real hope for passing his objective is if (a) the Dreamlands can be reached by one of the first two gates (very low chance), and (b) he can get to that gate quickly. Not easy with his maximum base speed of 3...
What an Idiot: In-Universe, this was quickly adopted as the explanation for his player's horrific luck with die rolls. As well as one very defining event. As the above thread says, just because you can use a bullwhip to snatch something out of a cultist's hands, doesn't mean you should. The something? Dynamite. Lit dynamite...It also became the reason for a 1st edition Arkham Horror house rule by the campaign master — Jack is always SAN 3 and STA 7 at the beginning. Come 2nd Edition, it became official for him...
Badass Bookworm: He has a high Lore stat, decent Sneak skills and a lot of Sanity points. His standard ability also reduces Sanity losses, making trips to the Asylum highly unlikelynote and being Devoured even less likely, as that requires losing all Hit Points and Sanity at the same time.
Took a Level in Badass: Under normal conditions, his passive ability only reduces involuntary Sanity losses, not voluntary ones (e.g. from spells). However, if he successfully completes his personal quest, this expands to cover all Sanity losses, allowing him to use books and spells all over the place with few (if any) penalties at all. Built correctly, he can dual-wield Shrivelling spells and curbstomp almost any enemy that doesn't possess the Magical Immunity trait.
Luck-Based Mission: She has kind of the same problem that Pete has (although even less time — her fail condition is the doom track reaching four). In her case, she needs to get an Ally to pass her personal story. The problem is that short of getting a nice amount of monster/gate trophies (not likely to happen in the short span of time she has to pass), she needs to get lucky with whichever location encounters can elicit the current game's Allies. Oh — whereas Pete's fail penalty is pretty minor (he can't get any more Allies, besides Duke), Lola's fail penalty is losing a point of maximum Sanity. Suffice to say she never wants the Herald to be Ghroth.
Unwitting Pawn: In his personal story, getting enough clue tokens makes him realize this, "failing" it. However, both outcomes for his story involve losing all his current monster trophies in exchange for a boon, so whether this is really a failure depends on whether you want money right away ("pass") or more clue tokens in the future (the alleged "fail").
Spirited Young Lady: It's not certain whether she's in the usual age range now (she looks like she could easily be in her late 20s), but she was definitely this during that age range (and before), and she hasn't lost her passion for adventure.
Game Breaker: All those clue tokens she accrues as the game goes on, along with her ability to share them with anyone, regardless of where either one is, makes it ridiculously easy to get a seal victory. Unless Yibb-Tstll is the Ancient One, that is (caps everyone's clue token limit at 5).
Deader than Dead: Monsters Yorick kills and spends as trophies don't have to be recycled back into play. Mind you, if the game runs out of monsters, the Ancient One awakens on the spot...Although if you have enough critters (i.e. from every single expansion that contained monsters), that's not likely to happen.