Enter the username and password of your Instagram account.
Click on "Authorize".
Select "Download Zip" and click "Start Export".
Once the backup is complete, click on "Download your pictures".
Create an automatic backup with IFTTT
IFTTT is a free online service allowing you to automate actions (recipe) on your various social profiles. You can create an IFTTT recipe to automatically backup (on Google Drive or Dropbox) every photo posted on your Instagram profile.