This strategy was a combined effort of me and burrito (okay, it was mostly burrito). For both hard badges you will have to take two seperate runs.
For the destroy 7,000 enemies badge, you will consistently want to choose the "grow" upgrade until you are big enough that if you go right in between two upgrades, you get them both. When you start doing this, go through the armor and +1 ally, or the +1 ally and grow (it doesn't really matter which). When you get to the final stage, you will want to fully release your allies (holding down the mouse) and let them do all the work. When you pick up an ally, release the mouse for a second, then hold it back down. It is very hard to lose using this strategy.
Now, for the more difficult badge in my opinion, the speedrun. For this one, you will want to pick up the speed upgrade 90% of the time (if you really need health or something, go for that if you want). try to memorize where ships spawn, and learn to be fast getting in and out of the circle. This youtube video by "ChromeGamer" really helps vizualize the strategy. http://www.youtube.com/watch?v=pjKN7Pv8Ohs