To unlock 'The fall of a Titan' you must complete the third mission (South China Sea) on Battlefield 4, on any difficulty.
It's a decent length mission, probably 25-40 minutes on hard difficulty. However, don't be put off by hard, as hard is fairly straightforward.
With regards to weapon loadouts, I'd recomend the starting AR and grabbing a DMR from your first weapons chest, as it makes the headshots/scoring bonuses incredibly easy. I'd always switch to an LMG/Sniper combo at the first chance you have.
Just follow the mission to the end, and the achievement will unlock in the sequence between levels.