To unlock the Shroomtender Jerkin, you need to complete the Defender of Necrom achievement. This is a pretty easy achievement to finish, especially if you have a friend to help, and it usually shouldn't take too long.
You need to defeat the six World Bosses contained within the Necrom chapter. If you're skilled enough to solo these bosses then that'll make things even easier for you, but don't worry if this is not the case.
You can simply wait around near the World Boss and it's very likely that more players will soon come along, and together you can take the boss down without much trouble. You can also try asking for help in the Zone chat or in a guild to speed things along.
There are two World Bosses in the Telvanni Peninsula, and four in Apocrypha. Below are the locations for all of the required bosses:
