750(ish) deadmau5 LED helmet

Hi there! So I have this behemoth of a project (deadmau5!) I'm working on for an halloween event using 700-800 rgb common cathode leds and I could really use some advice on how to set them up. As a test I've been making a 75 LED sign for the same event which has been giving me a lot of problems creating the right colours. When i connect 5 together to make white (1*330 ohm resistor per red diode), they work fine. but when I connect a lot more, they turn red. This is the sort of problem I could really use some help with.

I've attached (hopefully it worked) a photo of the basic LED layout I'll be using for the helmet, as well as the data sheet for my LEDs . I plan to control them using the Uno, and using a 7 pin numberpad for inputs. I'm not looking to do anything fancy like using shift registers to make animations (I don't have enough time), just a few static images for the mouth and eyes I can flip through using the number pad. If anyone is interested in helping me out I'd really appreciate it!

The Arduino cant afford such a high current.

"When i connect 5 together to make white (1*330 ohm resistor per red diode), they work fine. but when I connect a lot more, they turn red."
Suggests to me that your voltage is dropping too low for Green & Blue to turn on.
Usually that is a result of not enough current available.

How does the Arduino fit in? Will it be controlling transistors or drivers such ULN2803, or shift registers with high current capability such as TPIC6B585, to select the groups of LEDs to be turned on?

Hmmm if the current is too high for arduino what would you recommend? I was hoping to be able to have the majority of them running at the same time but not all. I was able to get around 175 5mm red leds to blink with the uno, so I figured this many wouldn't be a problem. I have little to no experience with transistors and shift registers, but if you could point me in the right direction on what I should learn that would really help out.

I can't say exactly what you have to do, but you must use an external power supply.

"Hmmm if the current is too high for arduino what would you recommend?"

Transistors and/or shift registers.
Post a diagram that shows how many you want to control in each group.