You will receive a +5 boss weapon (Riven +5) as the reward for handing over the beast heart (from Ixillis XV) to the undying king. This won't cause the achievement to unlock however. Now, you need to upgrade any boss weapon to +1, unlocking the achievement. As for crafting boss weapons... Upon killing either "Singe" or "The Ent" (depends on your world generation) you will receive a crafting material which can be used along with ~600 scrap, ~7 Lumenite Crystals and the boss material.
1. Kill Ixillis XV to receive beast heart
2. Give heart to Undying King to receive Riven +5
3. Craft any boss weapon using:
~7 Lumenite Crystals
1 Boss material (First available are from "Singed" or "The Ent")
4. Upgrade a boss weapon to +1
Farming Lumenite Crystals
Because each person's world is unique, I am unable to point you to a specific checkpoint to farm at. However, I can give you an important tip from my own experience.
Pay attention to the spawns near your checkpoints! If there is a special weapon very close by, then you can kill that special enemy and then reset the spawns to farm crystals. Personally, at my "Pan Flautist" checkpoint in Yaesha, I was lucky enough to have a special enemy spawn right beside my checkpoint. Close enough that depending on how close the spawn was (the spawn slightly changes each time you reset the enemies at the crystal, but the enemy types will stay the same), he could be within aggro range without me even having to move. It should also be noted that at least for "Pan Flautist" the enemy spawns did not go away even after clearing the area's boss. I'm not sure if this is the case for all areas however, so consider doing some farming before killing the boss.