I keep returning to "Supergirl" by Michael Green, Mike Johnson and Mahmud Asrar because the art is quite wonderful. Unfortunately, ten issues in, that's still the only thing "Supergirl" seems to offer.
Asrar's strong work easily makes "Supergirl" #10 one of the best looking books in the DC lineup. His grasp of Kara is well considered and appropriate. She looks effortlessly like herself in every panel and as a result Asrar is able to push her expressions and make the most of her emotional resonance. Black Banshee's "flamedragon" design is wonderful and the armor that Supergirl wears as well as the other costumes seen in this issue are some of the best she's ever looked. Dave McCraig's colors are equally smart -- evocative and sometimes slightly psychedelic as the story calls for it.
Unfortunately, the story just can't live up to the visuals. Exposition heavy and extremely overflowing with narration, Supergirl's voice feels like she could be any random character. Additionally Black Banshee (and crew) sound affected with their "ye" and "yers" and nothing else to identify their accent as being a of particular region. The result is a personality-less Supergirl and a cliché villain.
In some ways, the writing feels like a throwback to more classic comics, where the protagonist narrates everything they're doing as they do it on the page, and if that appeals to you stylistically, this might be an okay book for you. I don't happen enjoy it in even in my classic comics, so it hits like a lead balloon.
The plot is painfully standard. Some big bad (Black Banshee) has trapped Supergirl inside him -- because she thought it would be a great idea to give him all her power thus overwhelming him with it. Instead, it just made him stronger (as one might expect) and unlike everyone else he consumes, Supergirl is apparently not fully devoured. Convenient. Supergirl has no power left and then miraculously (and also conveniently) finds a little power within, allowing her to fight back. Black Banshee seems undefeatable in one panel and then a few panels later she's cutting his head off with ease.
The story feels particularly uninspired because it appears that some of Supergirl's memories are driving her experience inside Black Banshee. For example, she thinks of some armor and is then wearing it. This opens up all sorts of possibilities for how Supergirl could cleverly defeat "the dragon." Instead, after telling us she's basically powerless, she conjures up a sword with some remaining power, jumps on Black Banshee's back and disposes of him. It seems like an opportunity completely missed for a far more interesting and engaging story.
Both unimaginative and overly written, this book falls down in every area that isn't the visual. A good comic needs both unfortunately, and so this book ultimately fails.