This can be achieved on your first real mission to go destroy the four cars in the garage. Before you start the mission, go to Harry's on the Northwest of the map and buy hand grenades and Giuseppe's place for Molotov Cocktails.
Start the mission and drive to the mission marker. You should be able to get (1) SPEED on the first straight away. Hit your parking break on the final turn toward the garage and get (2) DRIFT. A little further are a few ramps, hit one for (3) JUMP. Drive in between the buildings straight ahead and run over the guy patrolling near by for (4) VEHICLE KILL. Run West and find three enemies. Throw a Molotov at one for (5) FIRE KILL and a grenade at another for (6) EXPLOSIVE KILL. Kill the last guy with a firearm for a normal (7) KILL.
Now go inside and replenish your Molotovs and throw them at the four cars for (8) DEMOLITION. Now more enemies will arrive. Kill all but one, getting at least one (9) HEAD SHOT. Get to the final guy as best you can without taking fire and when you get close enough you will go into a fist fight mechanic. Now beat him down for (10) MELEE
Now just finish the mission and achievement unlocked.