There are 37 rings in total to be collected around the map, when you jump through a ring it will turn green and that's how you'll know you've collected it. Below is a picture of all of the rings around the map, you can open your map by pressing the
button.
I also show all rings in my Achievement Walkthrough in one quick run starting at 0:35 seconds into the video for those who prefer video guides.
https://imgur.com/wjNeueb