There's lots of hints in the video description on how to achieve the sound:
Dark Sun combines a warm and clean digital delay algorithm with a lush Hall reverb, and the ability to route the two in just about any configuration you could want. And, you can shape the EQ of the effect, add saturation, or lush choral modulation, or use Dynamic Expression to control the mix of the effect with your playing.
Then:
A complement of filters, gain, and modulation round out the feature set. Applied only to the wet signal, they can totally re-shape the character of the effect. Use the Low Pass Filter to soften and warm up the sound, or the High Pass Filter to cut big low-end repeats, allowing you to use high mix settings without overpowering your playing. Saturation adds gain for pleasant lo-fi effects, tape-like saturation, or shoegaze-style distorted repeats. And, the modulation section can be assigned to the delay, the reverb, or both.
All of that can be done pretty easily on the Axe-FX using just the delay and reverb blocks in a parallel effects chain.
For the dynamic expression portion you can tie the envelope follower to the level control of the last effect in the chain, or put a volume block at the end of the chain.
