I would suggest playing on the Jungle level for this achievement.
I noticed that if I DID NOT hit any springs/jetpacks/trampolines I saw a lot more monsters than if I was hitting power-ups. If I did not see a monster by the time my score was at 3,800-4,000 I would die and start over.
There will be times when you will get lucky and see a monster around 1,800 but then it's likely that you will not see any monsters until 50,000 or so.
If you get into a situation where you can pass 4-5 monsters at once and are unsure, try shooting one of them to make a path for you to safely progress, if you think it's too dangerous and that you might die, you probably will.
After you play the game a while you will start to notice patterns and should be able to anticipate where the monsters will be and how many of them there will be.
Tips: Once you get to the quick moving platforms around a score of 50,000-55,000 that's the hardest the game will ever get. If you see UFOs, kill them as quick as you can since they will likely kill you. I made it to a score of 80,905 and saw 34 monsters and 7 UFOs.
Hope this helps.