Presumably you mean a barrister/trial lawyer rather an a solicitor? A corporate/contract lawyer in Commonwealth legal systems would typically be a solicitor (I work with an awful lot of them!).
But the actual plot of the show is kind of the reverse - she's supposed to be a competent state prosecutor - a deputy district AG in fact! Who is very much a trial lawyer. And then goes to join this corporate law firm as a "superhero specialist" - which is going to be a less demanding and stressful position, frankly, considerably better remunerated, better hours, and more support staff at your beck and call (even for a mascot - law firms do sometimes essentially have these, but they make sure they support them well to avoid being made to look bad). The show does weirdly make it so the corporate law firm seems to provide weak support for Jen, which isn't very plausible but still.
I think it really comes down to the show seeking to characterise Jen as "messy" personality-wise (which is very relatable and humanizing, sure), but it doesn't really land for me, because they could have made her a deadly wit in court, and messy in her personal/superhero life just fine - it's not like they're short of examples! That describes basically MOST lawyer shows! Certainly LA Law, The Good X shows, Damages, Ally McBeal, etc. etc. etc.!
If they get another season at some point (which seems unlikely, sadly), hopefully they can make her hit as hard in court as she does outside of it!
She's already a deputy district AG in LA, which is not a position an incompetent or inexperienced lawyer is particularly likely to have.