This song follows a few different chord progressions which can be easily broken down:

Pre-Verse - This progression comes before the verses (which has no guitar at all). The chords are:

C minor - Bb Major - F minor - C Minor - Bb major - F Minor - C minor

Notice that there are fast muted strikes, often between chord changes. The trick here is the mute / strum the strings whilst changing between the chords. This can be a bit hard to get right at faster speeds. One solution is to palm mute with your strumming hand at the same time as muting / shifting hand position with your fretboard hand. This will further help control string noise while you make the chord changes.

Chorus - This progression is a little more straightforward (no muting):

C major - A Minor - C major (G note in bass) - C major - A Minor - E major

Then build up with F minor chord and go straight into the pre-verse chord progression again.

The rest of the song is just more of the same progressions repeated. The only other new riff in the song occurs before the last verse / chorus. It is a progression of octave chords:

Octave Chord Progression - As you can see here, the same chord shape is used to shift between different positions. It's a lot like playing a typical powerchord, but skipping the middle note.

The trick to playing octave chords is to control the strings properly. This means muting the middle string with your first finger. That muted string is still strummed but it will be drowned out by the fretted notes either side. You can also use your thumb to mute the Low E string if you find it helps keep string noise down. Curl your thumb over the edge of the fretboard (from behind) so it lightly touches the Low E string, muting it. Check out the Core Skills section on thumb-muting for more about that technique.