iOS 8 pretty much killed my iPad 2. I sucked it up though and hoped iOS 9 would help but sadly it did not. Anything past 7.1.X on an iPad 2 is just awful. 512MB of RAM is the issue. After 4.5 years of my iPad 2, finally got an Air 2 during th Staples promo. So happy I did.
You can try restoring it as new, but I really didn't see a difference when I did it (multiple times).