For this achievement you need to reach one million points in multiplayer. It doesn't have to be with someone from your Steam friend list, it can be random people online as well. But you have to get the 1,000,000 points yourself, it's not cumulative between the players, nor will you get the achievement based on the other player's score.
One million points is not too hard to achieve, however: You can get more than half that one the first stage alone. Though playing in multiplayer, a lot of points is split among the two players. A general tip is to try to free as many prisoners as possible and staying alive until the end, as this will give you tremendous boosts to your score.
When you get to the first mission boss, try to keep your vehicle intact until the end, as that'll give you another 300,000 points alone. Also, as soon as you see the big explosion that signifies a form change of the crab boss, stop shooting it and stay to the right until you've rescued a total of 10 prisoners on the bridge where you fight the boss. Then fire the last, few rounds at the boss to kill it, and you're likely to be about halfway to this achievement already.
After this, just continue through the game, making sure to save prisoners as often as you can, and you should have this achievement before the game is done.
If you have a friend to play with so you can communicate, this achievement will be even easier. And it might be that you have to do this with a friend, because there aren't many people playing Metal Slug 3 online randomly. But you could get lucky and find some random games, like I did.