I wrote a Instagram Reverse Proxy API which supports CORS, pagination and limits (opens in new tab)

1. The following will give you access to the same data instagram provides. https://instareproxy.herokuapp.com/<user>/media/

2. Limiting the amount of images to be sent. https://instareproxy.herokuapp.com/<user>/media/?count=10

3. Using jsonp https://instareproxy.herokuapp.com/<user>/media/?callback=fo...

4. Using pagination: Each response has url links to the next and previous page, you can use that to traverse through the results.