Follow the fingering and picking here. Notice the logic of the picking. We do all downs on the descending notes, even though some are on the upbeat. This is to get a heavy sound and feel. The double down pick in the pull off figure of measure two is done because of the logic of picking 16th notes as down-up-down-up, and if one note is not picked because of a hammer or pull, the picking continues as it would have been if the note were picked. 

This subject is covered in great detail and with many accompanying exercises on page 27 of Troy Stetina's "Speed Mechanics For Lead Guitar", a book that should be used by any serious metal player. Read the Guitar Principles review...