Here is the full list of all 48 Cobra Kai: The Karate Kid Saga Continues trophies - there are 38 bronze, 6 silver, 3 gold and 1 platinum.
Complete your first Karate Challenge
Start a Cobra Kai Campaign
Finish Mini Golf and Arcade level
Found your first collectible
Throw an Enemy into the Basketball Hoops
Finish off your first of many Skeleton enemies
Start a Miyagi Do Campaign
Unlock all other trophies
Start a second Campaign with the other dojo after finishing the story with one dojo
Beat Cruz with a Special Punch
Smack Kyler's face into the floor with a ground attack mounted on his back
Finish Demetri with Hawk or vice-versa
Finish Tory with Sam or vice-versa
Finish Robby with Miguel or vice-versa
Finish Johnny with Daniel or vice-versa
Beat Yasmine using Tory or Sam
Finish Tom Cole with a Kick
Finish Sid off with Johnny or Robby
Beat Armand with Miguel's Jump Skill
Hit a Crane Kick on Kreese
Finish Daniel with Johnny's Cobra Ultimate
Finish 5 Hippie Hipsters with Grab Attacks
Finish 5 Fat Skeletons while they are in the air
Finish a Speedy thugs with a running attack
Beat Kreese and reveal the true story
Clear all City Missions
Buy your first upgrade
Buy 50 upgrades
Upgrade any Skill to the maximum (including Mastery)
Upgrade 4 Skills to the maximum (including Mastery)
Complete Karate Challenges group Warming Up
Complete Karate Challenges group Skill Master
Complete Karate Challenges group Combo Freak
Complete Karate Challenges group Environmentalist
Complete Karate Challenges group Specialist
Complete Karate Challenges group Surgical
Complete Karate Challenges group Rivalry Dominance
Complete Karate Challenges group Karate Champion
Unlock 30 Collectibles
Unlock 60 Collectibles
Unlock 90 Collectibles
Throw an Enemy at the screen
Finish an enemy smackin his face in the ground
Finish any Story level without being hit
Finish 3 Baseball Bat Skeletons with a baseball bat
Make all Tournament brackets nameplates fall off the panel
Parry 10 attacks without being hit
Get 120 Hits in a single combo