Watch the Alice's Grunge online guitar lesson by Angus Clark from Hard Rock Survival Guide: Rhythm
The grunge period was kind of a bleak period for guitar heroes, but Alice in Chains were really more of a hard rock band in flannel - and I like it! So, here's that signature syncopated rhythm for you, with a couple of other parts that evoke the chord motions that defined that era. One thing to pay attention to here is how the heavy part is featured in the overall arrangement. You have a very specific role to play vs. the drums and bass and so forth. So don't overplay. Stick to your part. This is a great opportunity to get this right hand muting together at a very reasonable tempo. Things are going to get harder as we move along, so enjoy the slow tempos while they last.