Hello PareshRaval3,
We understand you're having an issue with Game Center achievements.
You have come to the right place and we are happy to assist you.
With that being said, only certain games are supported by Game Center. You will see the icon underneath the game or you may also see "Offers iMessage App". You may also contact the app developer for more information on why your achievements aren't updating.
How to contact an app developer - Apple Support
1) Open the App Store on your iPhone or iPad.
2) Search for the app, then tap it. If you can't find it, tap the account button
or your photo at the top of the screen, tap Purchased, tap "Not on this [device]," then tap the app.
3) The app's product page appears. Scroll to the Ratings & Reviews section, then tap App Support. If you don't see App Support, make sure that you're signed in with the correct Apple ID.
Access your Apple Arcade gameplay data on all of your devices - Apple Support
If you don't see your gameplay data on a device
If you can access your gameplay data on one device but not on another, you might need to check your settings. Make sure that you have an iPhone or iPod touch with the latest version of iOS, an iPad with the latest version of iPadOS, a Mac with the latest version of macOS, or an Apple TV with the latest version of tvOS.
Check your settings on your iPhone, iPad, or iPod touch
1) Make sure that you're signed in to iCloud with the same Apple ID that you use on your other devices.
2) Make sure that you're signed in to Game Center with the same Apple ID that you use on your other devices. Go to Settings > Game Center to see the Apple ID that you're using with Game Center.
If you still don’t see your data and you were playing on a different device, check your settings on that device.
If you need further assistance after following the links above, please don't hesitate to reach out.
Thank you for contacting Apple Support Communities.
Cheers!