Supremacy is a Skirmish/Multiplayer game mode where your goal is to completely eradicate all of the enemy's engineers, commanders and structures. This includes the player's ACU, and any SCUs, but excludes mobile factories like the Fatboy, even though a fully operational base could be rebuilt from one, and non-engineer units with engineering suites like the Mantis. These games often take a longer time to finish, especially if one doesn't make use of every unit in their arsenal.
A good strategy for this game type on a large map is to take a number of small, fast units and a few engineers and hide them throughout the playing area. If the opponent takes out the main base, they will still have to go looking for these little units. While they do that, a new base can be built (although as they could easily make sure that you could hold none of the mass extractor points this will be slow). However, these new, smaller bases typically won't have the resources or strength of the original base, making it more vulnerable and harder to operate, and this tactic is almost certain only to delay your inevitable defeat, although it will likely annoy your enemy. Hiding units with stealth may help you to escape detection as well.
Overall, the likely approach to this game format will be likely similar to an Assassination match, except with far less importance ascibed to keeping your ACU intact, and very similar to an Annihilation game, where all units must be destroyed.