Open Instagram and go to the person’s profile
Check their posts to see who has liked them
Tap the likes count on a post to view the list of accounts that liked it
Look at their comments and tagged posts for activity clues
Check mutual followers and following for shared interactions
Search their username in Instagram’s activity areas if you have access to their account
Note that Instagram no longer shows a public “Following Activity” feed
You cannot reliably see everything someone likes on Instagram unless you have access to their account or their activity is visible on a post