Thanks to "Dark Devil Wolf" who suggested a simplified version of the guide by "morph Xlive", from TrueAchievements.
For this achievement, there are two parts: max out your weapons and purchase all of their moves.
The first is the worst.
1) While you should put any weapon XP into either the Scythe or the Gauntlets as early as possible (I highly recommend having the Scythe be the first thing you buy), there is no point in focusing on training the Sword as you will get an end-game item that maximizes it automatically.
2) Wait to do focused weapon XP farming until after you reach the Iron Canopy.
3) Once you reach the Iron Canopy, get "War's Glory" (In a chest near the northwest of the map; available after you gain access to the path leading to the boss fight against Silitha) and equip it to the weapon you want to focus on.
4) Go to the entrance of the path to Silitha's lair (the spot that had a magic barrier showing five spider symbols blocking the path); from there head South and jump down the ledge with demonic growth and enter the room there.
5) Lure the spiders there (in you preferred way, whether running through or just shooting once at a couple), exterminate them all.
6) Follow the path backwards, up the demonic growth towards Silitha's Lair path. Take one step past the light grey flooring and walls, then turn around and return to the room with the bunch of spiders. They will have respawned for you to wipe out again! (If they don't, you needed to walk just a tiny bit further).
7) Repeat until your weapon is maxxed out, then switch to the other one!
For the Sword, it will get instantly maxed out when you complete the Armageddon Blade, so don't waste time trying to level it up faster.
Fortunately, by the time you finish this you should have TONS of souls to give to Vulgrim in exchange for all of the weapon moves, so that part is super easy!
Note: If you are able to get your hands on the Harvester (which looks different and gives +10% Souls... but is not available via proper gameplay on PC versions), note that while it does take the place of the Scythe it is treated as the same weapon as far as this achievement is concerned.