IOS 8 or later on iPhone 4

Unfortunately, This is not possible due to current App Store limitations unless someone else with a jail broken iPhone that you trust has a copy of it that you can grab. One problem with dealing with the Apple App Store is that older versions are forever lost due to Apple's App Store polices. We should be giving concerned feedback to Apple to address this issue too, not just the app developers. So it looks like your best option if you need to have the Mint app, is to read up on the latest jailbreak, and insure your jailbreak path, then update your iPhone to the latest iOS, and then re-jailbreak it. The good news is that there is a untethered jailbreak for both iOS 5 and iOS 5.0.1 for the iPhone 4 as referenced in my comment above.

The final iOS rev for iPhone 3G is 4.2.1, and you could always save a backup before upgrading and restor to the 3.X version if 4.2.1 was too much of a hog.

Hope this helps!

Edit: This thread says its not even worth it. 4.2.1 is crippling to the device.