This has been happening since last weeks open beta, mainly with chocobo's but also with the odd mob. It continues to happen regardless of in game graphical settings.

AMD FX6100 processor
8GB DDR3 RAM
Asus m5a97 pro motherboard
Nvidia GTX 660 TI GPU
256GB samsung evo 840 SSD
Corsair 750W PSU
Regularly updated chip sets/BIOS/drivers/etc.