This Achievement is
Gunsmith worth 25 gs.
For this achievement you need to level one of your weapons up to level 10. When first going through Mass Effect 3, whether you imported a character or not, you can only upgrade a weapon to level 5. To keep upgrading the weapon, you need to import your saved Mass Effect 3 character that has completed the game already. The game will then allow you to upgrade your weapons to level 10.
To upgrade a weapon head down to the Shuttle Bay and look for the Upgrade Terminal. You can also look for the Upgrade benches throughout the levels. Remember, in your first playthrough, you can only upgrade a weapon 5 times.
Thanks to Deception975, You can achieve this without ever playing Single Player. When playing in Coop, you can use the Credits you earn to purchase boxes. Yes they are random, but if you get the same weapon 10 times over, you will pop this achievement. In this method, you do not have to beat the Single Player campaign.