She wouldn't "laugh" his blasts off. I'm sure he could do some damage. It's just that he has some issues to overcome.
1. Her flight. She's no speedster by any means, but she does rush down a lot of characters during confrontation.
2. Her forcefields.
http://tinypic.com/view.php?pic=35ism6g&s=5
http://tinypic.com/view.php?pic=mj2z2d&s=5
http://tinypic.com/view.php?pic=24etc0n&s=5
I'm not sure exactly how her energy bolts could really "vaporize" his own beams, though. I want to say that his beam would be detonated and diffused on contact, but he's weird and it's just kinetic energy so idk. In a comic they would likely just lock up in a single energy beam struggle ala DBZ.
3. Her durability
She's taken hits from Wondy, Superman, the Astro Force, Luthor w/ gear, etc.
4. Her grit and subsequent rage.
Kory is a warrior, and she can take a hit before returning in full capacity - and more likely to be mad. When Luthor punctured her shoulder she was still running around extracting Supergirl from the rubble and had the gull to ask Kara to cauterize the wound with heat vision. One quick lazer surgery later and she was back in action.
5. His own durability. One blast and he's as dead as Deathstroke's son. One light jab and he would be lucky to survive.