Moco actually has two Jedi as parents that raised her from birth, they married in secret and when Moco was born it all came out. Because of the great things her parents did during the war the Jedi counsel was forgiving and let her parents stay together and raise her in the ways of the Jedi. When finally after many years her time came to take her final Jedi tests she was deemed by the counsel not strong enough in the force to take them without possibly being killed. She had control of the force, the full list of moves she could easily preform like push, pull, lift, jump and even lightning that her parents taught her without the counsel knowing. (They had the full Revan belief where no power is good or evil its just how you use it) Its just that Moco was just not as strong in doing these things as her fellow Jedi peers. It took far more discipline to call on the force and concentration for her to do these things. So the counsel out of concern for her well being would not let her take them, instead they were going to give her a position at the Jedi Temple as temple-watchmen/guardian.
For Moco this was not at all what she imagined would happen to her. Her parents tried to tell her she would still one day become a Jedi Master it would just take more time. But because of being turned down from her final tests even after being born into the order she took this as a sign from the force that this was not her path. With love and respect she left the order on good terms and went in search for her destiny. After a few years of searching she came across the idea of the Republic Military. After much meditation she was sure this is what she should do. She entered into the military as a normal citizen feeling she would get special treatment if she told them she was trained by the Jedi. She excelled in every training aspect and graduated only a short time after entering. With her skills as a Force user and military mastery that's how she came to be placed in Havoc Squad.
With all this training she's gotten her personality still shows through though. No matter what her commanders say she makes the final decision. Moco is fun and joking like her parents but still firm in demeanor. She's very expressive when she can be and always fighting for the Light Side even if her path sometimes leads through the Dark Side.
As far as her fighting style is concerned, she uses her cannon to mow down enemies primarily but she still carries her Jedi lightsaber clipped to her belt (in my mind). And the force-moves often find a way into the fight, a little force push or zap here and there never hurt anyone.
Here's a little side-by-side comparison. The in-game model next to my painting.
Aaaand here is another character from the Old Republic if you are interested: