Enable All HiDPI Modes

Yes, this is possible:

Reference

First you need to get SwitchResX.

After installation, you then click System Preferences > Other > SwitchResX > select your Mac / Monitor from the right column -> Custom Resolution > and click + button to add a new resolution.

Now you need to select "Scaled resolution" inside the select option field & enter the resolution inside the scaled to Text field. So lets say if you want a 1920 x 1080 Hidpi setting, you need to create a custom 3840 x 2160 etc.

After all, just click save and then restart it, once you restart your mac, you should be able to see the new hidpi setting under display setting.

The answer is that it is not possible, when the 13" MacBook Air's higest native resolution is 1440x900. It simply does not support 1280x800 or 1440x900 HiDPI modes, since it does not have a retina display or a display with enough pixels to do HiDPI. For the MacBook Air in its current form, it would need to have a LCD display with at least 2880 X 1800 pixels to enable HiDPI modes.

To do HiDPI 1280 x 800 you would need a display with resolution of at least 2560 x 1600, again, not possible on the 13" MacBook Air's display.

As noted in Signs in Mountain Lion point to "retina" display MacBooks sooner than later retina displays and graphics require 2x the resolution of normal graphics and displays.

You can add HIDPI on any Display Monitor with or without retina using Quartz Debug: http://www.osx86.net/view/2224-quartz_debug.html (It's official, extracted from Apple's Xcode).

The problem is that it will only enable half native resolution for HiDPI.

For instance: my MacBook Air is 1440x900; with this tweak, I could pick 720x450 (Native Resolution / 2).

The hidpi on OS X is only for 200% increased size, not just a 110%-150% to fit a resolution near your native resolution (like 1280x800, etc.).