One tip:

If you are farming alexandrites, it's better go to low level zones, middle La noscea or western thanalan, that's fates is more easy to complete because there are few peoples doing it and the mob's hp is low.

Usually i kill one mob 1 hit + dot or 2 hits, and you need 10 mobs to complete the fate.

My favorite zone is summeford farms, because there are a fate chain, where the last boss is "chupacabra", i got 6 alex doing that fate, one for the first fate and the second for the last one.