If you know that certain update is available of your already downloaded app on your Windows Phone, these steps will explain how you can force an update.
- Go to the Store (formerly Marketplace) on your Windows Phone.
- Search for the app that you know has an update available.
- Tap on this app to see its product page.
- You probably only get the option to Share this app at this moment.
- Tap the back key.
- Tap one more time on the app in that search result.
- Now you should get an update button right next to the Share button as well.
- Tap on the Update and your are one step ahead of your Store notification tile.