If you're completely done with Instagram and want to wipe all memory of your activity from the network you can do so by deleting your account. Think carefully before choosing this option as Instagram will permanently remove your profile, photos, videos, comments, likes and followers when you do.

Before deleting the account you may want to save a copy of all of your photos and videos. You can do this with a third party tool called Instaport. Enter your account details, choose an export method and it will save your pictures for you.
Once saved, you can delete your account with the following steps.

1. Go to Instagram.com, log in and go to the deletion page 
2. Scroll down and select Delete Your Account 
3. Instagram will ask for a reason as to why you are deleting your account before it lets you 
4. Re-enter your password and confirm you would like to permanently delete your account