Gladiator's powers derives from his confidence, which will continues to decrease during his match with Big Barda!
Although she was the best Female Furies, I doubt she would exploit his weakness in the beginning. She's been portrayed as a noble warrior like Wonder Woman, only wanting to defeat or kill her enemies through fairness following her escape from her home world. She could tank his physical attacks, and she could also absorb, deflect, or protect against his heat vision and cold breath with her Mega-Rod given her history with the Justice League. Her hand-to-hand is far more than enough to bring Gladiator down for the count! And if that's not enough, then her Mega-Rod could finish him off, or expel him to another location!