Here is the full list of all 34 Dreadnought trophies - there are 14 bronze, 16 silver, 3 gold and 1 platinum.
Collect all other trophies in Dreadnought
Defeat wave 10 in Havoc
Defeat a wave of Havoc in less than 45 seconds
Complete 1000 games
Add a Tier V ship to your Fleet
Win separate matches as a Dreadnought, Destroyer, Artillery Cruiser, Tactical Cruiser and Corvette
Win a game with a Legendary Fleet
Kill 100 enemies in Team Deathmatch
Destroy 10 Command Ships in Onslaught
Add a Tier II ship from Oberon, Jupiter Arms, and Akula Vektor to your Fleet
Win 25 games of Onslaught
Heal 1,000,000 damage
Kill an enemy that an ally has debuffed
Win 25 games of Team Elimination
Earn 150 assists
Kill 25 enemies with your secondary weapon
Finish 10 Team Elimination matches without dying
Kill 10 enemies with your secondary weapon
Kill 25 enemies while in a Squad
Kill 3 or more enemies in under 10 seconds
Kill 2 enemies within 1 second
Eliminate a player in Team Elimination with a Fighter Jet
Win 25 games of Team Deathmatch
Heal back to full life after dropping below 100 health
Complete 100 games
Win a game with a Veteran Fleet
Shoot down a Fighter Jet in Team Elimination
Customize a ship's appearance
Kill an enemy while dead
Complete 5 games
Get a Kill with an Assist from a Squad member, and vice versa with the same player
Add a fully researched ship to your Fleet
Finish a match as the highest-scoring player on your team
Customize your captain's appearance