As in title.

Also note that when you earn a gold star at an elevated difficulty, you also receive all of the lesser stars for that level. So if you Perfect a level at Extreme before playing it on Normal or Advanced, you'll still get three gold stars. You don't have to replay levels at lesser difficulties unless you want to.

[Developer here]
Also - please note that they're more like "challenges" than "difficulty modes", so we're *slightly* subverting some people's expectations -- You're not actually intended to be able to beat advanced/extreme right away.

The idea is they're there for you to go back to after a few missions, with new challenges (not just more enemy HP) to try out, so that if/when you want to "grind" you have new content to experience rather than just farming the same old battles over and over, and if you just want to keep plowing ahead you can either settle for blue stars (Azra takes damage) or drop down to casual difficulty.

Here's a blog post about the general design philosophy:
http://www.gamasutra.com/blogs/LarsDoucet/20110822/8248/RPGs_challenge_and_grinding.php

Thanks all