Rare mobs spawn randomly throughout the world. They are on internal timers that are randomised so there is no way to tell when a rare will next pop up. There is however a limit to how many rares can be up in a zone/area at any one time.
If you are searching for a particular rare to pop your cheevo and it isn’t up, you should go around the rest of the zone and kill the other rares that are up. This will clear the spawns for that zone and then when the rares start respawning, the one you need may spawn.
Most of the rares spawn at a particular location and stay there waiting to be killed. However some rares like to wander around. The locations provided for the wandering rares will be the middle of the general area that they spawn in, so you can run around the area spamming your target macro.

SWITCH SHARDS! – Different rares are up on different shards, so switch shards at each location and check them all.

There are a few addons that you can use to help you hunt rares. I have never used them myself but I have heard good things about ‘raredar’. The addon will tell you how close you are to a rare location, so you don’t need to remember where all the rares spawn.

Macros: Because I don’t use addons for hunting, I instead rely on target macros and waypoints/maps – I have macros for each zone that I click/spam while I’m hunting to target any rare that is up near me, I have copied these macros into each of the zone pages so you can use them too. Most of the macros cover more than one zone just to save space.
Be Aware: Sometimes the name of the rare mob is slightly different than what is written on the cheevo, also the macros don’t always enjoy apostrophes or dashes (you may need to retype these), this is why the full name of the mob may not be in the macro, but the target will still work. They have been fully tested!
Reset: After a server reset (shard downtime usually lasting a couple of hours, generally on a Tuesday) the rares will take a while to populate, you may want to wait 4+ hours before hunting. The normal daily/weekly resets (4am every days) do not effect rares.