Okay first, you are not better than beginner yet. Don't label yourself.
1. Practice slowly, and make sure you don't lift your fingers off too much. The only way to make this a habit while playing fast is to learn it slow.
2. For independence, work on chromatic patterns like 1-3-2-4, 1-4-2-3, etc. Also use 'the spider', where you fret every consequent fret without lifting your other fingers, even while fretting the next string.
3. All exercises when started slowly with gradual progression will build speed. You need patience and dedication, there's no shortcut. Only push the tempo up when you have it down 100% at the current tempo.
Everything's Eventual (tm)
Scarborough Fair/Canticle (Cover)