I think you need more practice... you sung everything from the head, with almost no breath support. Did you hear about the concept of singing with the diaphragm? There's a lot of online resources on it or you could ask a friend who sings to explain it to you.

Without proper support, everybody's singing sounds weak, and you still have to achieve this by what I've heard. After 0.40, when the notes are higher, you must push the air through your vocal cords with your diaphragm (the upper part of your gut, where the bottom of the lungs is) so your throat can concentrate on holding notes. If you push the air with your throat, it won't sound good. Your voice is clearly shaking and struggling to hold itself together, especially at the sustained note at 1.25. High notes are demanding if you want to sing them good, and you need stronger muscles than the ones in the throat to push air through your cords if you want good ones.
Again, look through the forums and the internet, you can find many sources on proper singing technique. It will be best to get a vocal coach to teach you in person - or if you have friends that know how to sing, ask them to show you how.
I don't know what you mean by "I'm trying out", but if it's some sort of choir or band you're interested in, wait a little longer 'till you improve.