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:
Contamination King (15G), RATONA NAVAL PORT - 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 4 spinning Bosses from mission 07, but now they got much more AP. I suggest using a tank with all TE defense, use 2 powered autocannons with reverse magazine, easiest boss of all.
Below is the video how this fight looks like.