NOTE: I have had people comment saying the dashboard trick to save your Titanite Slab doesn't work. The game has been heavily patched since release, so there is a chance it won't. If you take a chance with the trick, it is at your own discretion, so be careful and make sure your dashboard as soon as the achievement pops.
The dashboard trick still works as of 30th December, 2023Also, 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. The same can probably be said for the rest of the weapon achievements as well.
When you get to Sen's Fortress, there 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 its defeat, you are rewarded with a lightning spear. At this stage in the game, it's the only Lightning Weapon that you can find. 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 decent damage and like most spears you can hold your shield up to block AND attack at the same time! Very easy-to-use weapon for novice souls players, or those wanting a slightly easier time.
For obtaining the items needed to upgrade the weapon, here's what I found:
-- In the Great Hollow there are 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, the 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 the bonfire to reset them. The reason was 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, but it's up to you.
-- 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. You best use backstabs to finish them off quickly if you choose this method.
-- 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 at the beginning of the game. (walk on the floor and it will drop down into the new Boss chamber)
It would also be 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, though 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?