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:
Marsh King (15G), PASK FIELD - Middle East
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 Liv, the small floating robot, that shoots laser beams and energy jammers in all directions, when it getclose to you about ~200 meters it will charge at you dealing massive damage. The best tactic is to use 4 heavy bipedal with 2 long range Rifles, FCS 500 range, TE defense above 4000, High speed missiles, generator with high jamming ressistance, just shoot untill he drops, you can take 2 additional shields on back for protection.
Below is the video how this fight looks like.