Well I dont grow this particular species and I only have one Coryanthes, but mine is growing like a weed. From what I understand these are all fairly easy to grow. Dark conditions (mine is in the lower end of the Phal lighting spectrum and has very light colored green leaves, aka it is getting a little more light than is probably needed!) and TONS of water are needed for these guys. They are also heavy feeders. Heck, just buy the darn plant and then you can be the Cory. speciosa expert for the OB!! Nothing ventured, nothing gained! Good luck!!
Unlike Coryanthes machranta (the other Brazilian Crths.), Crths speciosa is very hard to grow; they live in consortium with some ants in nature ('Aztec' ants), and they became very sensitive to all kind of fungi and bacteria in cultivation. Other problem are slugs and snails. If you want to try to grow Crths speciosa, you'll need follow Steve tips and take care with the diseases and pests I mentioned. Good luck!