DAVE THE DIVER

The earliest possible time to get this trophy is when you beat the game, since a boss is the very last thing you do!

The following boss fights occur while playing through the story. Just to note I'm only listing the bosses that have their own marinca cards. There are other boss fights against John Watson that do not grant a card and are also entirely story based):

Giant squid
Giant wolf eel
Phantom jellyfish
Heliocoprion
Kronosaurus
Yawie

The rest are optional, but none of them are difficult to find.

The first mechanic to explain is stormy night vortexs. The very first stormy day that you encounter in the game, Sato, the dude that introduced the Marinca cards to you, will come up to your boat and explain that on stormy nights a vortex appears at night time which allows you to fight a dangerous creature and earn a rare card.

There are 3 of these fights, and they can only be battled at night when it is stormy. If you check the weather app on your phone it will show you the weather for the next 3 days if you have some other task you wish to plan for. Don't worry if you fail an encounter, you can simply retry again on the next stormy night.

Truck hermit crab
Mantis shrimp
Great white shark Klaus

Side quests:

Clione queen:
Eventually a character will appear at bancho sushi named Maki who will ask you to make her a dish. Once you satisfy that requirement she asks you to catch 5 cliones for her, and gives you a net to do so. Cliones are only found in the depths and it will take you at least 2 trips to find all 5 of them. Upon finding the 5th one the clione queen will attack you. Feel free to hire Maki at the restaurant after the quest, she is a decent early game cook with a little investment.

Goblin shark:
Once you make it to chapter 3 and unlock the sea people village, Tenzhen gives you the task of doing quests for the people of the village and getting them to trust you. While working on this you may notice some children playing with a ball to the right of the mirror where you spawn.

Eventually, on the second or third trip to the village, you will notice they aren't playing anymore. Talk to them and they give you the quest to retrieve it from the megamouth shark out in the blue hole depths. Once that is done talk to them.

After another few trips to the sea people village (you probably already have progressed the story from doing other quests), you will again see them not playing. Talk to them and they inform you one of the children ran off to see the lake. Follow this quest line out into the depths and enter the sea people chamber (you need the pickaxe to progress inside), and the boss fights awaits.