You can keep your speed up by making the ground gently wavy about in the middle of the screen, which gives you time to move up to high gates without losing speed. Aim for the bottom of high gates and the top of low gates and you shouldn't have to deviate much from the middle unless it is for a tunnel or to avoid a red gate. It's possible to get the hard badge by staying close to the middle, keeping up speed (50+), and maximizing the bonus from tunnels.
My strategy for the Sparta mode: a quake tower (or two) with max fire rate, and a fully upgraded grenade launcher. The Spartans didn't make it half way.
The key to the hard badge is to beat the intermediate bosses (at level 10, 20, 30). If you concentrate on buying only Energy Infuser upgrades until level 10, you should be able to beat that boss easily. This will give you 5 upgrade points, so you can get Antimatter Shield and two interest upgrades. Then save all your money until level 20, and buy as many Energy Infuser upgrades as possible before starting level 20. If you beat at least the first three intermediate bosses, you should be able to reach 20% interest and get most of the useful bonus upgrades. Good luck!
This is an average game. The hard badge is a bit of luck: if you don't get a few speedups in a row right in the beginning it is much easier. I scored 115 on my third try at infinite mode.
Not a very hard hard badge, but the game is fun. The bosses require timing - you have to hit them between their shots. If you keep them moving at a reasonable speed, this is even easier to do.
For everyone complaining about not getting badges: PATIENCE. Just wait on the end screen until you get them, it takes about 30 seconds after the game ends for them to be awarded.
Level 4: line the outside of the halls with centaur. For any melee wave, they get decimated pretty good on the way down the line. I don't recommend vampires, because they cannot fly over the fortified walls.
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