Screwed-up ace pilot with a traumatic childhood spent with an abusive mother and absent father that caused her self-loathing, self-destructive ways; who drinks too much, has a messed-up personal life and keeps hurting and being awful to the people in her life, except for the deep father/daughter relationship with her commander, but who is also very spiritual and religious and has a prophesized special destiny, first conveyed to her by a Cylon with whom she has a weird love/hate relationship.
If that is a cliche, than so is every character ever in Trek, and 99% of other characters on TV and in movies.
The added Starbuck specific backstory doesn't make it any less of a cliche.
Well if that's how you define "cliche" - whether you can fit the character into an over-simplified description that can apply to a number of other fictional characters - than, as I said, 99% of all TV characters are cliches, including pretty much every Trek character ever. Only, Trek fans and writers prefer to call them "archetypes", because it sounds cooler.
Kirk - swashbuckling hero admired by his crew and irresistible to women
Spock - outsider who comments on the human condition / mixed race child with identity problems
McCoy - grumpy doc with a heart of hold
Scotty - everyman
Khan/Nero/Shinzon etc. - maniac bent on revenge
Data - outsider learning to be human & looking for his origins/family
Lore/Shinzon/every Mirror Universe character - Evil Twin
Worf - noble savage from a warrior race
Riker - swashbuckling ladies man
O'Brien - everyman
Guinan -
Magical Negro
Odo - outsider looking for his origins/family & learning to be human; geeky loner with an unrequited love for his best friend
Kira - brave warrior with a dark past; also a heroine that a charismatic villain is trying to seduce, a cliche going back to 18th century sentimental novels by the likes of Samuel Richardson, and every fucking Gothic novel ever, to contemporary SF/fantasy (Xena/Ares, Buffy/Spike etc.)
Quark - lovable rogue with a heart of gold
Chakotay - spiritual Indian (see: Magical Negro)
EMH - grumpy doc with a heart of gold; outsider learning to be human
B'Elanna Torres - mixed race child with identity problems
Tom Paris - bad boy with a heart of gold
Seven of Nine - outsider learning to be human
T'Pol - outsider learning to be human
You get the idea.