The World boss fights can only be accessed via special sorties, you can fill up your gauge by completing 6 standard sorties and be victorious on them.
The other method to fight Bosses is after a season, there is a 1-hour time period where all bosses are present and can be fought.
You can tell whitch boss you are fighting by looking at the name of the map:
Desert King (15G), DOZUR DESERT - New Frontier
If you are looking for a certain Boss, you can select a faction that you want to fight, there is 8 boss in total each one in the different location on world map.
In this map you must fight Last Boss, but now he is in his floating suit, and bombard you from sky, to drag him from there i suggest using autocannons and sniper cannons, few direct hits with autocannons will do the job, when he dropped, he will start using laserblades at close range, you just need thermal defense and shoot him to death with autocannons and sniper cannons.
Below is the video how this fight looks like.