An "arpeggio" is nothing else but a chord played note by note separately. Here we have D minor, E dim7, F major, G minor and A minor. Left hand is playing one inversion of the chord (arpeggio) and the right hand is playing a different inversion. You can clearly see those shapes on the scale charts when you download the lesson. Please note that left hand is also playing tapping. This is what we call "tapping from nowhere" as we tap the string without previously playing anything with the pick. Everything is played in 16th triplets so keep that feel over 4/4 time signature in 120bpm.
You should practice this very slowly until you get used to these shapes. Also a good amount of distortion is welcome for this kind of stuff so you don't have to hurt your fingers until you get all the notes out clearly. While it is posibble to avoid noise by muting non-played strings with both hands, those lucky ones that have string dampener should definitely use it here. If you don't have one then even a sock can help like I used on the video :)
Have fun practicing this one