I got this Achievement last night by simply blowing up Micky Desmond's car with him a in it, before he got out of the Hill of Tara parking lot.
I blew up the car using a Tommy Gun and aiming it at his gas tank. He'll try to drive away, but keep your aim steady and on his gas tank, and he'll be toast (pun intended) by the time his car makes it to the street.
I probably could have used the grenades or the Molotovs I was carrying to achieve the same results, but since I was using a Thompson SMG for the raid on the pub, it's what got the job done for me when I went to get him.
Now you are probably wondering exactly how I got completely armed to the teeth before going after Micky Desmond, considering my house and all my money got completely burned out. For the answer to that question, see my solution for getting the Exporter Achievement
After your house burns down, go to Joe's like normal, but before heading up to see him in his apartment, make a stop in your garage at his place, and use my solution for the Exporter Achievement
to make some quick cash. Then load up on guns and ammo at Guiseppi's and at the Army Surplus store, before going to take out the last of the Irish mafia.*** NOTES *** 1.
It's also possible to make some quick cash, by stealing one of the expensive cars cruising the streets of Empire Bay, and selling it, instead of going all the way to Joe's to get the ones out of his garage.2.
If you do not feel like going through all the effort of drumming up quick cash to finish this mission, there is always the MP40 and the grease gun at the pub. Killing the bartender or one of Micky Desmond's goons to get either one of those guns, will work just fine. And then use one of those to blow up the gas tank on his car.3.
When you go see Joe, there is a Playboy on the floor next to his bed. Also there is another playboy in the back of the Tara pub (down the dead end hallway). If you are trying to score the Ladies' Man
Achievement, or just like to look at nudes of someone's grandmother, you will be in luck twice more while attempting to nab this Achievement.4.
Without giving away any spoilers, near the end of Chapter 14 you are going to need to come up with a HUGE
amount of money - you can probably guess how much before Chapter 14 begins. The quickest and easiest way in the game to earn huge sums of money, is exotic car exporting - which is no longer possible starting with Chapter 14; and consequently, is next to useless until just before going to the Tara pub to finish of the Irish. So sometime between your house burning down near the end of Chapter 11, and before the start of Chapter 14, make sure you gross a huge bankroll, or trying to earn the rest of the money you will need, makes the game pretty frustrating.