Bjorn is the easiest and should be your first target. Shoot him in the head with the turret on the left, and prioritize shooting down his boulder and fireball attacks. Eventually, you'll be able to hop on his head and stab him in the eyes for a bit.
Nokturnus is no joke. Familiarize yourself with his moves above all else. The best advice I can give is to make sure your characters have Artful Dodger and Ace Evader in their skill trees. Without those upgrades, it's very hard to avoid his one-hit-kill attack from above.
Atlas is unlocked after you beat all of the Veteran versions of the main story bosses (They're called Grudge Matches on the level select screen.) He has a stupid amount of hit points, but there's an easy way to bring him down: Terry! Equip him with a Mighty Armlet (critical hits on weak points +5%), Wrecklace (Coup de Grâce damage +7%), and Titan Belt (damage to weak points +6%).
During the fight, use Terry's Falcon Slash (R1 + Circle) to create copies, then repeatedly spam Gust Slash (R1 + Square). This will rapidly build up his tension meter, at which point you can become invincible, activate his Coup de Grâce, stun Atlus, then repeat the process. You'll need to have Terry at a high enough level for him to kill the boss in time, but otherwise it's easy. (This tactic is super useful in most of the game, by the way.)
Zoma is the biggest jerk of them all. He should be your final target. You won't win unless you have a high-level party and equipment to offset his magic. I gave my characters a Bunny Tail (reduced freeze time +40%), Lucky Dragon's Wing (magical resistance +20%), and Raging Ruby (lower damage, more criticals +5%). That finally did the trick.