NOTE: I have had people comment saying the dashboard trick to save your Titanite Slab doesn't work. The game got heavily patched a few months ago so it may not work now. If you take a chance with the trick it is at your own discretion, i can't be blamed as this originally worked but i've also got comments saying it still does, so be careful and make sure you dashboard as soon as the achievement pops. The dashboard trick still works as of 29th of April, 2015
Also, as another user has mentioned in the comments. You can simply get a friend to drop you the weapon when they are in your game and the achievement unlocks, so if you have awesome friends then it cuts out a lot of the work. Same can probably be said for the rest of the weapon achievements as well.
When you get to Sen's Fortress, the will be a room you HAVE to go through after chasing boulders down 2 sets of stairs. This is where you meet your first mimic (a monster disguised as a treasure chest) and upon it's defeat, you are rewarded with a lightning spear. At this stage in the game it's the only Lightning Weapon will have found. All you need to do to gain this achievement after is to upgrade it to a Lightning Spear + 5 and 'POP' achievement is yours!
To upgrade this to a + 5 you will need :
Lightning Spear + 1 = 1 Titanite Chunk
Lightning Spear + 2 = 1 Titanite Chunk
Lightning Spear + 3 = 2 Titanite Chunk
Lightning Spear + 4 = 3 Titanite Chunk
Lightning Spear + 5 = 1 Titanite Slab
You can upgrade this to a + 5 yourself at a bonfire (if you have the smithing boxes purchased) or any Blacksmith
The weapon itself (currently using) is pretty dam good, does a decent damage and like most spears you can hold you'r shield up to block AND attack at same time!
For obtaining the items needed to actually upgrade the weapon at all here's what i found:
-- In the Great Hollow there is at LEAST 2 chunks found while descending the Tree, i can't name specifically where but i found 2 along with other coloured chunks.
-- The Royal Sentinals, the two big guys in Anor Londo in the hall right before the boss fight, drop chunks (you'll know which ones they are because they can also use Healing Miracles) I personally farmed these for an hour and only got 1 chunk, best bet is the bonfire outside of where you obtain the Lordvessel (the massive women) and run down the elevator, run through the room you fought the dual bosses and kill the first knight, then run back to bonfire to reset them. Reason being it took too long to kill the other one while the Black Knight on the stairs shot arrows at me, so it was faster to kill one and run back.
-- The Darkwraiths in Lower New Londo drop chunks as well, though very rarely. These enemies can also drop the Titanite Slabs, which is rarer still. Best use back stabs to finish them off quickly.
-- So far as much as i can gather there is ONE definite Titanite Slab drop per game, its when you revisit Undead Asylum the second time (it's optional) from the Boss which is underground in the room you fought the original Boss in the beginning of the game. (walk on the floor and it will drop down into the new Boss chamber)
It would be also wise to note, unless you are going to be personally using the weapon for something, gather all the necessary materials required to upgrade and do it IN ONE GO. Once you do, and the achievement pops DASHBOARD IT! Reload the save and you will still have the Titanite Slab which is the hardest to obtain.
(My friend and I have confirmed this works, thought he used a Blue Titanite Slab)
Of course you can get better Lightning Weapons if you upgraded them from scratch, but hey who wants to waste resources on that?