If you don't see the achievements on your Profile screen, please go to the Trips and try to pull the list with your flights down for an update. Wait until the flights are synchronized, restart the app, and check for the presence of badges. You will find the screenshots with the details explained below.
Go to your Trips → Swipe down to update the account data.
Wait till the "Syncing" message is disappeared.
Go back to your Profile → You should be able to see all your badges back again.
Also, there are different types of levels as you can see below the icons there are some numbers. For example, airplanes with 3 digits mean you are at the 3rd level (every 5 planes it changes differently).
Go to your Trips screen → Swipe it down for an update.
Then go back to your Profile → Scroll down and you can see your achievements back.