But she's seen his soft side, too.
"On camera, he's like this big tough guy, but when the cameras come off, he's a big teddy bear," she tells PEOPLE of her mentor, 52. "He's so sweet and he's loving and he's hugging and he's kissing. And he's just like, 'You're awesome!' "
Cowell, who's competing against his co-judges Paula Abdul, Nicole Scherzinger and L.A. Reid, has a good reason to dish out the positive reinforcement. "He's trying to give you his motivation," Amaro says. "He's trying to help you as much as he can. He's being Simon."
On Wednesday night's episode, which marked the first time viewers could vote for the contestants, Cowell told her, "Right now, you're the one to beat."
"I was shocked, and I was happy," Amaro, 19, says of the compliment. "I was like, 'Wow, he sees that I'm working really, really hard.' "
Having proved her talent, Amaro says she wanted to mix things up a bit on Wednesday, which she did by singing the Eagles' "Desperado."
"He told me already that I keep him guessing," she says. "He says what he thinks I'm going to do I never do, but that just makes him feel like I'm trying to push myself out of my comfort zone and making him proud of me."