Flash rendering native Shape/Sprite/MovieClip is great for a trivial number of simpe animations, but if you have many or complex animations going at once, it hits a wall pretty quickly.
In the instances where you determine that rendering is the bottleneck (profiling is your friend) then you can get much quicker performance by creating a Bitmap as a 'view' in your game and using BitmapData's copyPixels function to blit BitmapData representations of your animation frames into that view every frame.
In my latest game, I'm doing exactly this, for exactly this reason. I'm taking the desired MovieClips, stepping through their frames and caching bitmapData representations of each frame by using BitmapData's draw() method to render the frames at load time (which is a little slow) and then using copyPixels to draw them in the view at run time (which is super fast).
Nothing is for free of course, so you have to be mindful that you are trading CPU cycles for memory space in this case, and if you have a lot of long animations, your apps memory usage will skyrocket pretty quickly.