Not really a solution, but just some tips to help you get all three awards.
First off, let's discuss what you should equip. In addition to the weapon itself, what specializations you choose might help this achievement go faster. The M16A2 is one of the most accurate assault rifles, but mediocre in damage. Thus, the Assault Rifle Training perk (lower bullet spread for more accuracy) is not really needed; go for Magnum Ammo on Spec. slot 2 to give it a slight but helpful damage boost. As for Spec slot 1, you'll probably want the 4x scope so you can attack from afar (useful for the killstreak award). Reflex scope is very nice too, though.
First award: Achieve a killstreak of 5 without dying. Although 100 kills requires more time investment, this one might be the hardest for some players. It's very easy to die in BFBC2, so killstreaks can be frustrating to attain for some. If you get streaks fairly often, you should keep Magnum Ammo on to kill faster. If you have trouble staying alive, two things can help. One is to equip Body Armor for Spec slot 2; it reduces damage you take. It's only slight reduction, so don't go running in front of rockets expecting to live. Another is to have a buddy go Medic so he can be dedicated to keeping you healthy. If you die and he defibs you, keep in mind that it resets your killstreak.
Second award to tackle: Get 8 kills in a round with the M16A2 SA. With Magnum ammo, you should have no problem getting at least 8 kills with your M16. If you are defending on Rush, a 4x scope lets you take some time to pseudo-snipe oncoming attackers.
Last award: 100 kills with the M16A2. This doesn't require anything other than persistence and dedication. Again, as general advice, equip a 4x scope to attack from afar and use Magnum Ammo to down your foes faster. Depending on your skill and luck, you might breeze through your enemies and rack up kills fast, getting the award in just one night. Others might take many, many game sessions to accomplish this.
Hope this helped!