Here is the full list of all 48 Bloons TD 5 trophies - there are 38 bronze, 6 silver, 3 gold and 1 platinum.
Pop 250,000 Ceramic bloons
Pop 250,000 Camo Bloons
Destroy 1000 ZOMGs
Destroy 2000 BFBs
Complete the Protect Monkey Town Special Mission
Destroy 5000 MOABs
Complete the MOAB Madness Special Mission
Complete any track in reverse.
Earn all other trophies in the game
Pop 250,000 Lead bloons
Pop 50,000,000 Bloons
Achieve glorious victory on any map on Impoppable difficulty
Earn an Impoppable medal on 25 or more maps
Collect 50 Tokens
Activate all upgrades for Starting Cash
Activate all upgrades for Pierce
Activate all upgrades for Attack Speed
Activate all upgrades for sell %
Activate all upgrades for Starting Lives
Activate all upgrades for Big Bloons Sabotage
Activate all upgrades for Ability Cooldowns
Win all Tracks on any difficulty
Win all Special Missions
Get all Special Agents to Pro Status
Purchase and upgrade to tier 4 all Specialty Buildings
Complete the Full House Special Mission
Complete the Highlander Special Mission
Complete the Special Agent Only Special Mission
Complete the Fast Upgrades Special Mission
Complete the Short-Lived Special Mission
Complete the Covert Pops Special Mission
Complete the Wizard Lord Special Mission
Complete the No Escape Special Mission
Win 10 Random Missions
Win 50 Random Missions
Win 100 Random Missions
Win 200 Random Missions
Win 250 Random Missions
Earn 10 gold medals in single player.
Earn 20 gold medals in single player.
Earn 30 gold medals in single player.
Earn 40 gold medals in single player.
Earn 50 gold medals in single player.
Earn 5 gold co-op medals
Earn 10 gold co-op medals
Earn 15 gold co-op medals
Earn 20 gold co-op medals
Earn 30 gold co-op medals