Disclaimer March 2020: Instagram no longer offers any choices in camera and users are obliged to use the camera within the app. For tips on how to take good photos for Instagram, check out this article.
Instagram - Use the phone's default camera app
If you are experiencing issues with Instagram's advanced camera, you can easily switch to the phone's default camera app. The procedure is as follows:
Open the Instagram app.
Go to the Profile tab.
Tap on the Menu key (3 vertical dots).
Go to Settings > Camera
Turn off "Use Instagram's Advanced Camera".
Instagram camera settings
How to change instagram camera settings - Best answers
This document, titled « Use Your Phone's Default Camera When Using Instagram », is available under the Creative Commons license. Any copy, reuse, or modification of the content should be sufficiently credited to CCM (ccm.net).