A few weeks ago I noticed what looked like corrosion on my rear shock and swingarm. It looked like the battery leaked and ate away at the parts below it even though I took it out and checked it. I didn't see any leak at all. Either that or I ran over something and it got on the bike. Either way, I'm trying to see if my rear shock is trashed, and how do I clean these parts up.

 

How long is your vent tube on the battery? Make sure it is long enough to drip below any hard parts.
If it's clear-coated aluminum, the BEST solution is to remove all the clear coat and start over. There is a clear-coat remover (that is like a prep for aluminum; specifically) you can buy. (Can't recall the name.) Shine it, and shoot it with high quality clear-coat.
If it's anodized or "hard plated," you can likely clean it with some baking soda (a "basic" pH) and water, which will neutralize the battery acid. The anodize or hard plate should be pretty much OK. Just don't scrub the #@$% out of it with a 3M Scotchbrite pad or anything!
If it's painted, you may likely need to strip it and re-shoot.
The battery acid should not have affected the performance of your shock, but give it a good cleaning.
My 2-cents.