The ensuing battle is brutal and one of the best fight scenes the show has ever produced.
And then she immediately collapsed in the fountain from exhaustion as Alex came running up to her.
Supergirl and Superman search through the Fortress database and discover the sacred trial by combat.

Credit: Bettina Strauss/The CW
So, Supergirl, stepping up as Earths champion, challenges Rhea to a duel.
I love the fact that Superman is letting Supergirl lead the way.
Thanks to a dream about Mgann, Jonn wakes up from his coma and jump right back into action.
Lillian thinks Lena can modify the weapon to disperse lead instead of Kryptonite.
The Luthors approach Superman and Supergirl with this solution.
Superman and Martian Manhunter finally bury the hatchet and head out into the streets together, too.
Even though Supergirl is weakened, she continues to fight because this is her planet, goddamn it!
The Daxamites ships start flying away, and Rhea dies.
We knew Supergirl was a real superhero, but this more than confirms it.
And Winter makes sure we realize how heartbreaking it is.
Supergirl pleads with Mon-El to hold on for a bit longer while she gets him somewhere safe.
While the entire city is able to celebrate winning, Supergirl cant.
She just lost the first person shes ever loved.
Not only that, but everyone around her is with their loved ones.
Before flying off to be by herself, she tells Alex to never let Maggie go.
So, Alex does the logical thing and proposes to Maggie on the spot.
(Do I think Alex and Maggie should be getting married so quickly?
Hell no, but hey, theyre currently riding that adrenaline high.
Hopefully theyll come to their senses later.)
The next day, a despondent Kara goes to see Cat at the office.
Naturally, Cat knows just what to say to cheer up her mentee.
Unsurprisingly, this is what Kara needs to cheer her up.
A fire breaks out across town, and Kara runs off to save the day.
The finale ends by planting the seeds for several season 3 story lines.
First,we see Mon-Els ship get sucked into what looks to be a Phantom Zone wormhole.
It should survive the journey.
All I know is that Im intrigued and excited to see what happens next season.
The biggest problem with the second season is that it was missing a strong sense of focus.
The aliens-as-immigrants allegory was thought provoking, but it wasnt enough to hold the season together as a whole.