To get this achievement, you need to find the blacksmith designs for the fire and ice bows, and then craft them.
The ice bow design is located in the Cirith Ungol level. There is a platform you can push to knock out 3 boarded up areas, the design is in one of them.
The fire bow design is located in the Helm's Deep level. After the wall is destroyed, make your way up the left side, you will see a mithril crate. Blow it up (beserker) and the design is yours.
Fast travel back to Bree, make your bows and the achievement is yours.