When you get to Hendon Myre you will come across a little scientist named "Loton".
When you talk to Loton you'll see above his head a blue symbol, enter into that menu and you should have entered his "Reinforcer/Disassembler Shop".
From there simply find a weapon or armor of yours and you'll be given the option to reinforce the item. What you want to do is reinforce the item to +5 which will require you to have minimum 5 Ryan Cokes and some spare gold.
*Ryan Cokes drop from enemies on occasion in dungeons.
Once the item has reinforced to +5 the achievement will appear.
**Note that you can fail in reinforcing an item, so its better to have extra Ryan Cokes handy.**
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