"You must update to iOS 8.0" when trying to download apps on iPhone 4
Solution 1:
The last version of iOS that the iPhone 4 supports is iOS 7.1.2. You will not find any more software updates for the iPhone 4 beyond this.
This means you are unable to install any apps that require a more recent version of iOS (not all apps require iOS 8 and later), however it may be possible to download a previous version of an app that does support iOS 7 by adding the app to your purchase history using iTunes on a computer first.