7) Brainiac
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A recurring foe throughout Supergirl’s first season was Indigo, who was basically a female take on classic Superman villain Brainiac. It’s a nice idea to give Supergirl her own versions of her cousin’s enemies, but unfortunately Indigo and her associate, Zod stand-in General Non (descript), were poorly-realized villains. For season two, then, the show should just do away with the imitations and introduce the proper Brainiac.
Brainiac 5, in particular, would be a great addition. In the comics he has a creepy romantic interest in Supergirl, which would make for an interesting element to the new Big Bad. This Brainiac is also a pretty exciting character, as he later rejects evil and joins the Legion of Superheroes.
Speaking of which…