Here we have a short breakdown for the piece where the drums fade out.
I'd recommend using all downstrokes here. Any idea why? Well, if you look at all the D string notes, you'll see that they're palm muted. So since that's the case, I'd prefer to use downstrokes, since a downstroked palm mute has much more attack than an upstroked palm mute.
Be sure to practice this part (and all parts) with a metronome if you can. If you listen to this part in the full video, you can hear the drum's high hats playing quarter notes. Just as those high hats are keeping time, use your metronome to also practice at speeds that are comfortable for you.