To play guitar really, really fast — you must begin really slowly. Slow, methodical practice allows you to establish a strong foundation of skills to build off. Playing guitar passages quickly but sloppily is an inefficient practice technique that prevents progress by ignoring mistakes. It is easier to address mistakes by practicing deliberately and paying close attention to each note being played. If you notice a particular section is giving you difficulty, isolate that part until it is comfortable, then return to playing the whole part.
When learning any new guitar exercise or song section, a good tempo to begin practicing at is around 60 bpm. At this tempo, you should strive to play one note per metronome click. Continue practicing until you have played it perfectly at least 3 times in a row. If you mess up on your third time, reset the counter and keep going until you nail it. Remember, practice makes perfect!
Once you have played it perfectly 3 times in a row, increase the speed by 5-10 bpm. Continue repeating this process and you will quickly find your fingers becoming more comfortable with the exercise.
After reaching 120 bpm at one note per metronome click, you have succeeded at playing the exercise with quarter notes. If you want to keep improving (of course you do), set your metronome back to 60 bpm, but this time attempt the exercise with 2 notes per click — gradually increasing the metronome speed. Every time you reach 120 bpm, reset the metronome to 60 bpm and double your notes per click.