1. When playing the palm keys, try to keep your fingers curved as much as possible. This will facilitate moving from those high notes to the front key notes. The knuckles should move inwards as you press the keys, whilst keeping the tips of the fingers curved as much as possible.
2. A frequent issue beginners encounter is that the saxophone tends to tilt to the right when using the palm keys. Press the keys with a more "downward" action.
3. Ensure your thumbs are supporting the instrument and that your strap is not too low.
4. Keep an ear on the intonation. The embouchure should not change.
5. Avoid biting too hard on the mouthpiece.
6. Ensure good breath support to allow for good tonal quality.
Work on these notes by extending the D, E, Eb and F major and minor scales and arpeggios to two octaves. You could even break the scales and arpeggios into smaller exercises, focusing on the upper notes.
Enjoy your playing!