Here is the full list of all 10 Keep Talking and Nobody Explodes trophies - there are 4 bronze, 5 silver and 1 gold.
Disarm each type of module at least once.
Defuse "The First Bomb".
Defuse all bombs in "The Basics" section.
Disarm 100 modules.
Defuse all bombs in the "Moderate" section.
Defuse all bombs in the "Needy" section.
Defuse all bombs in the "Challenging" section.
Defuse all bombs in the "Extreme" section.
Defuse all bombs in the "Exotic" section.
Defuse 100 bombs.