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