This article explains the issue with the likes count of a post when an organic post is boosted.
When an Instagram post is boosted, you might see a different number of post likes on Instagram compared to the number in Agorapulse. This is caused by the fact that
Instagram merges the like count for the 2 posts (the original post and the boosted post).
Right now, this is a problem of the Instagram API and there is no technical way for Agorapulse to overcome this - the technical explanation is that the Instagram API doesn't provide a way to traverse from an Instagram ad object to the associated Instagram organic media or in reverse (organic to ad).
However, if you connect your Instagram ad account we will be able to sync the boosted post, therefore you'll be able to see both posts (original, organic one and boosted) and their metrics.