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), MIYNSKY HILLS - Far 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 Exusia, similar to one from ACV, but now with more AP, the only powerful atack that can fast kill you is boost charge from the air, from the rest you just need Tank with all Thermal defense, use 2 powered autocannons with reverse magazine, 2 heavy gatlings on back to gain stability, the important part is to have good recoil ressistance so it won't stagger you.
Below is the video how this fight looks like.