What's the scary part?

If you would like to work over there then you should apply and the worse thing that might happen is not hearing back from them.

At least, if you do that, you would have a chance and more importantly, a good experience from which you could learn a lot.

I am a student, and I can completely empathize with how you feel. I can tell you that a lot of what I've seen is that it's one-hundred percent completely worth the stress and fear of rejection if even one long-shot (in your mind) pays off. I've had that happen to me firsthand, and I've seen it in other people. The more experience you have dealing with tough problems, the better you'll be thinking about them, and tough interview problems by extension. Just make your interview count as best you can, and step back and wait. I promise it's worth it.

Yeah. I've had several interviews, and am currently working as an intern at a startup, but I've never experienced any difficult algorithm-heavy/trick problems in interviews. One of the things that deters me from applying is just the fear as you've said but I'll definitely be trying for jobs that I feel are a little out of my comfort zone next semester, and I know it will be worth it.