This Solution is for those who have EXTREME trouble with this achievement and have a second controller...and don't mind being Matt Hazard's "bitch", (as the game refers to him) Dexter Dare.
The concept here is sort of like the "Beat The Game In Co-Op by yourself" but the inverse, you'll be controlling the second controller (Dexter Dare) INSTEAD of the main (Matt Hazard) controller. Kill off Matt in the beginning of the level by running him into enemies and bullets until Dexter is left, then simply play through as Dexter.
Try and die to use a continue near the boss and not AT the boss so that you can kill Matt off and have a stock of full lives if you continue. (Or just start a New Game and play through the first level racking up lots of extra lives).
Either way, use the above boss tips while playing as Dexter and once his third form is close to dying, summon Matt back in the battle by pressing A+X to steal a life and once the boss falls, the achievement should pop.
I have tried it both ways, legit and this method, both work, one is a tad easier because Dexter isn't the account you want the achievement for...he does all the leg work for Matt...maybe he really is his "bitch" after all...
Just saying if Matt dies during the boss fight, you'll have to redo the entire level in order to get another chance.