As with every achievement in this game, this one will take quite a bit of practice. You're going to want to survive to at least 250K without using a bomb, but if you get into a situation that you know you're going to die around that time, use a bomb. The multiplier that you keep can help you get points much more easily and you will hit 700,000 almost as quickly as you hit 600,000.
You get a bomb every 100,000 points. If you die your first time at around 400,000, this is where you will need skill to survive as the game gets more difficult. The trick to winning this game is to go around in a circle around the board and always shoot directly in front of you if the number of enemies is overwhelming. If you get surrounded by enemies, shoot your way out in one side and then go in your circle and kill them as they follow you. Beware of the blue discs that come out of the imploded black holes because they are faster than your ship: make them your priority.
If you play the game enough, you will learn the patterns and eventually you can win on instinct. Practice enough and you will eventually succeed.