The battery had died on my 3rd generation iPod years ago and I had long given up hope of resurrecting it. After finding ifixit.com I decided to give it a go and I'm chuffed to say the 'antique' is back alive!
As everyone mentions, getting the cover off is tricky. But don't be afraid to give it some force. You're probably not going to scratch it any more than it already is. The plastic told are soft enough.
However, the guide mentioned using the 'large opening tool' first and then the 'small opening tool'. However, the kit I ordered only came with two small opening tools, so that threw me off at the beginning. But I was able to get the cover off eventually – so it is possible using just the smaller tools.
Stick with it – you got it!