I originally thought this achievement was stupidly hard, considering I'm new to this game, but after some practice I came up with a method that worked for me.
I found that if you wait about 2.5 seconds at the beginning, then following his tail about half way down and then paralooping clockwise back on yourself, I was getting 17/19 link pretty often; eventually I hit the needed 21 link.
I've uploaded a video of said method in action, too.
This might not work for everyone, but I thought I'd throw it out there anyway. Good luck!