How does the new iPad's Retina Display affect its battery life?

As we all know, the new iPad has a gorgeous new Retina Display. And yet, it's advertised to have battery life just as good as the iPad 2's.

How is this possible? Doesn't the new display require a lot more power to run? Were any performance tradeoffs made (e.g. refresh rate), or did Apple improve the battery enough that it's irrelevant?

Your question's wording is a bit unluckily.

There is no previous iPad with the same battery capacity. It does not really makes sense to talk of an impact of a new display to the battery-life. That's not a reasonable comparison because the battery has been updated as well.

The retina display of the iPad 3rd generation

The new iPad uses 2.5 times the backlight power of the iPad 2. This is due to the TFT transistors of the high-res LCD display blocking more light. (source)

This also contributes to the heat emission. The overall performance however is only little affected, because Apple compensated the increased power drain by adding a 70% bigger battery.

(pictures 1,2)

Battery life is marginally improved overall. Basically it's a bigger battery. The extra power required by the higher quality screen, along with the GPU that is needed to power it is more than made up for by increasing the battery capacity by approximately 70%.

Rumours that the iPad 4 will include Fuel Cell batteries with a 14 year lifecycle that takes 3 years to charge are thus far unfounded.

See this interesting article for more info

excerpt follows:

Because of the increased battery draw of the MDM9600 and Retina display, Apple had to significantly increase the iPad's battery capacity. The original iPad had a 24.8Whr battery, and Apple increased that slightly to 25Whr in the iPad 2 while shaving off nearly 5mm of thickness. Though the iPad 3 is just 0.6mm thicker than the iPad 2, it boasts a 42.5Whr battery—an impressive 70 percent capacity improvement.

The revised three-cell design appears to be slightly larger than the battery in the iPad 2—each measures about 125 x 65 x 4 mm, according to iFixit CEO Kyle Wiens. The cells in the iPad 2 measure 108 x 63 x 2.7mm, so the iPad 3 battery is actually about 70 percent larger. Earlier speculation suggested that Apple had somehow significantly improved on the power density of the cells, but our calculations show otherwise. Apple was just able to more efficiently pack in the components—and increase the overall device thickness ever so slightly—to make the battery larger.