I figured it out. I bought a preset Logo Opener from Videohive.
You have to drop your logo into this thing and it animates it. But the preset composition size was small. So I changed the size of the composition and was able to scale my vector up and make it work.
When posting questions like this just a screenshot of the result is almost useless in diagnosing the problem. A better screenshot would include the Comp Window and timeline with the layer in question selected and all the changed properties revealed by pressing the U key twice. Also, since this was an imported file that is in question, if the footage item is selected in the Project panel then we can get an idea of the format, size, and other properties of the original file that may be causing problems.
You should not have to buy anything to get properly created vector files ti work perfectly in your composition. When you said zoomed in at 400%, if you meant scale factor and not scale of the layer then the behavior is normal, expected, and exactly what should be happening. Zoom Factor set to 400% means the comp window is using 16 screen pixels for every comp pixel. Zoom Factor set to 1600% means a single image pixel is displayed as a 16 X 16 block of screen pixels - so things are going to look pixelated when they are not. The only way to judge quality is to look at the composition window with the Zoom factor set to 100%. This is exactly the way Photoshop works.
Here's what I mean. A single Illustrator layer selected, scaled to 5174% and perfectly rasterized in a comp with the Zoom Factor at 100% scale. Note the layer size in the project panel. Everything we need to know to diagnose a problem.