Hello M8, it's not so difficult but you need the right tools.
Firs of, if I remember correctly there is no real bearing inside the pulley. There is a sort of autobrake system in it so it can freewheel when not needed.
Take of the pulley plastic cover plate.
There are two types, one with an internal hex and one with splines. Hopefuly you have the one with a hex.
Now on the alternator shaft there's also a hex. It's a 5/8 I believe, somewhere around key 10 in metric.
You need to hold that and then turn the pulley counterclockwise to loosen it. JEEP dealers have a special tool with a double hex to also grab the pulley internally. I ended up taking the whole alternator of my engine, take an angle grinder to it and then bashing it with a chissel and a hammer to brake pulley loose while a socket held the axle.
Since I already destroyed the old one I took it apart completely to know what was inside, the screachy noise you here is just from the 'brake' dust that has no where to go. The brake pad was still in good shape. Blew 150€ on the part. Next time it gets noisy I'll try drilling 2 holes in the front right next to the big hex and blow it out with compressed air. The plastic cover should be enough protection to keep ( rain -) water etc out.
