Easily boostable with a friend, each enemy kill counts as one point. With one player hanging back & the other killing you should unlock this around Stage 4.
The stage 3 boss in the sewer dropping mousers can be exploited for 30-40 kills before he times out if one player stands or jumps in a top corner while the boosting player concentrates on killing the dropped mousers.
UPDATE: Some additional information based on comments/feedback.
You need another person ONLY to start/play the game over Xbox Live.
Scoring is individual, not cumulative. Only the INDIVIDUAL with a score of 250 should expect the achievement to unlock.
I just tried this in a Private match and didn't get the achievement. We tried again in a Public Match and I got it. Might want to make a note you can't get it in a private match.
Might also want to point out you don't need to beat the game, it'll unlock as soon as you hit 250 points.
I hope this eliminates any potential confusion, I apologize for not being clearer in the initial post. I too tried to do this achievement in a private match the first time and forgot to include that detail, thanks ezekiel08. Hopefully this clarifies the achievement for people new to this game and avoids more negative feedback, thanks!