In order to get this achievement, you need to play the campaign until you get the Mod upgrade for your ship. At that point, any mods you have picked up will be available for you to apply to either your weapons or your Warframe (in your Arsenal screen, press Y on your Warframe or any weapons).
Mods have a number in the top right corner - these indicate how many points are required to place them. Your equipment, and your Warframe, have a certain number of points, which seems to be dependent on your level. For example, at level 8 my Volt I had 8 points available.
Broken mods (the ones that say "Broken" and have cracks) usually have a cost around 2 points. If you have 4 broken mods for your Warframe, and you are at level 8, then viola! Achievement for you.