I am trying to learn this by ear. I am used to playing mostly slower stuff so, since I am not used to playing fast, I am unable to figure out this particularly fast guitar part that starts from 02:11 . Thanks.

https://www.youtube.com/watch?v=sxvR3YZQyoA

Assuming a 6 string guitar in standard tuning, the pattern you're looking for is:
E|--15--12--11--12--
B|---------------------
G|---------------------
D|---------------------
A|---------------------
E|---------------------

...played in sixteenths over four bars (or in super layman's terms - just repeat what I wrote 16 times straight). Pick each note (i.e. no legatos or tapping) for maximum authenticity.

Check out some fastpicking tutorials on youtube, there are tons of them. Also just practice fingering (haha yeah I said it) the notes slowly to develop muscle memory.