To make this simple and fast acquire the jury rigging perk after level 14. The requirements are on this page.
http://fallout.wikia.com/wiki/Jury_RiggingOnce you have that perk it allows you to repair weapons a lot easier by using similar weapons to repair. This will make the process go by very fast. I was able to get it in less than 5 minutes after getting the perk. I just made a save, repaired weapons till I got the achievement, than reverted back to the old save.