Instructions
Become a firefighter. You should have the Handy and Athletic traits up, as well as Friendly or Charismatic. These are a good basis for a firefighter. Once you think you have a good enough rank in these traits to start, click on the Fire Station on the map. This allows you to become a firefighter.
Go out on fire calls and successfully complete missions. You earn your first trophy when you have saved two Sims from a fire, and it's the Firefighter's Trophy of Honor. It also comes with 100 experience points, which is a nice addition.
Complete the Gnome Invasion. The Gnome Invasion is an in-game event you'll go through as a firefighter, and once you've gotten past that part of the game, you receive the Firefighter's Trophy of Valor. This second trophy also comes with 100 experience points.