Install Latest OS X version with Internet Recovery

The best way is to boot into your current OS X install, and download the Mountain Lion installer from the Mac App Store. When the installer asks which drive to install to, select your second partition.

Internet Recovery is different to the Recovery HD partition.

Generally…

As long as you have a valid Recovery HD partition, trying to boot into Internet Recovery will instead boot your Mac into standard recovery mode.

Both recovery modes download OS X anyway…

installing Mountain Lion from within recovery mode requires an Internet connection to download the actual OS.

…so I recommend using the Mac App Store to install Mountain Lion as I mentioned above.

Disk Utility shouldn't let you remove the Recovery HD partition unless you are in Debug mode. It is unlikely that you have accidentally deleted the Recovery HD partition, and since you can select it when holding alt to select a boot drive, I doubt very much that it's gone.

The App Store Mountain Lion installer is the universal installer capable of installing on any compatible Mac. There is no 'different installer' for Retina or otherwise.

Using ISO

If you restore the ISO to a flash drive or other drive partition, you could ⌥ alt-boot from it and erase & install OS X.

^{In my example I selected a random DMG, however in your case you would use the ISO image as the Source.}

Internet Recovery

Yes, but only if you install the Internet Recovery firmware update for your MacBook Air.

Once you have, hold ⌘ cmd + ⌥ alt + R on boot to begin.

An image of OS X will be downloaded from the internet, and can be installed normally.