How come he could possibly know that Rachel will win the award herself and go onstage the second time so that he waits for it and does not strike when she goes onstage the first time?
He doesn't. Nothing in the scripts say he does know.
But Portman is a former (very well) trained special agent, now a killer. He knows how to go around safety measures, counter-measures, he knows how to navigate such events, it's even part of his training. He's smart and cold-blooded, he'll wait for the best opportunity. He already had a chance (maybe), when Rachel invited him in a private room, at her reception. He was disturbed, as Rachel refused his sexual advances, and called for help.
At the Oscars, if he misses the first opportunity (on stage, when she co-hosts the award with Reardon), he'll have another opportunity. He hid his weapon inside a camera. He can move around, unnoticed, he can aim and shoot from almost any angle. He has no need to rush, he can observe the surroundings, analyze, and wait for the best shot.
Even if Rachel doesn't go back on stage, she'll still be around, answering interviews, surrounded by people and cameras. Portman, if no one knew/discovered who he really was, would have been able to shoot, being close or not. I'm not even sure that people, scared by the 'bang' of the gun, running around, would notice or be able to identify the origin of the shot, giving him time to drop the camera and escape.
To answer comments, my understanding of the facts is:
when she went onstage the first time, it was his best chance. But he didn't even attempt it.
Nothing says if he was ready or not. If he doesn't take the shot, it's probably because of a lack of proper preparation. A pro won't take a chance, he wants to kill her in the spotlight and escape, it's not a suicide mission. It has to be perfect, from his POV.
He waited for the second one as if he knew it was coming.
He goes around all places, and can navigate every part of the stage. He may have heard something (even if we don't know). It's not in the script. And she clearly is the favorite for being awarded, so going back on stage is possible.
