This it relatively straightforward to do. From the main menu, select load out. This will let you access the 4 load out saves you can have, Alpha, Bravo, etc.
All you need to do is change one thing with each load out. Press Y to amend the load out, and for example, change grenades to a land mine, on the next one switch grenades to dynamite, etc. when you have altered all 4, the achievement will pop.
Note some of the weapons/gadgets are not accessible at the start, but can be accessed via searching bodies and finding them in the game.