Several users have reported that the App Store has not been showing updates properly, meaning that, although a badge indicates that there are updates available, the App Store says “Apps Are Up to Date”
How to fix:
You need to completely close the App Store app. To do that, double press your home button, tap and hold on the App Store icon, and then, when it starts to jiggle, tap the minus sign. Now hit the Home button again and open your App Store by tapping on the App Store icon.