The number of Instagram Likes you can unlike is not specified anywhere on the Instagram website or in their terms and conditions. A common assumption made by users is about 300, but delete Likes at your own risk. The bottom line is that bots monitor your liking activity, and if you appear to be using an automated system, you'll get banned. That's why it is best to delete Likes as if you were manually doing it. Some apps offer a frequency option to help protect you from getting banned, but that statement is not guaranteed.