To sing high notes, practice a smooth, balanced way of singing.
First, practice your breathing so that you get in enough air as you sing. The less air you inhale, the less connected your notes are. When you sing staccato, you are allowed to take breaths between each note. However, most singing must be smooth and connected as you move from one note to the next.
Then you also need to promote balance in the way you sing, start by taking deep breaths. Practice your breathing by timing yourself as you hold your breath. Swimmers know how to hold their breath well, so pretend like you are going underwater. In fact, think of a steady flow of air as the steady swim strokes you take through the water. You want to glide through the water effortlessly and make as few strokes as possible.
The more you practice the exercise, the more you should increase the intensity. Increase the number of minutes it takes to hold your breath. Eventually, you will inhale a very long breath that helps you sing smooth, steady notes.