The different levels present quite a variety of challenges. In particular, many of the hard levels really forced me to try something other than the same strategies that had worked on other levels, or on other TD games.
(1 of 2) The easy game plays almost like a tower-defense game, but to beat the hard game, you also need to learn how to aim the ultragun. The better you aim the ultragun, longer you can hold off upgrading your repair bay, turrets, and fighter bays. That allows you to upgrade the ultragun more quickly. Before long, you'll need the damage and fire rate of the ultragun to be fully upgraded.
Unfortunately, the make-or-break level seemed to be about a third of the way into the game. It took a while to figure out how to survive that far, but once I did, the rest of the game seemed relatively straight-forward.
(2 of 2) Try to kill the enemy ships before they get close enough to damage you. As others have pointed out, aiming is easier if you sell the initial fighter bay immediately. Without fighters distracting them, the enemy ships stay in formation and come straight at you. Don't get distracted if some get through though. Take care of the strays when you can, but be sure to get the incoming enemy ships that are still in formation, and easier to hit.
When the astroids appeared, I bought (and started upgrading) a laser turret to help with the strays. Later, I bought (and started upgrading) all the fighter bays, so the fighters could help with the mines. I finished the game with the ultragun damage and fire rate fully upgraded, the laser turret damage and fire rate fully upgraded, all the repair bay features fully upgraded, and the fighter bay max fighters fully upgraded, plus other upgrades.
sulaji84 - Directly above the Ultragun is a row of 3 hardpoints where you can build turrets. Directly above the middle of those 3 hardpoints is the Repair Bay.
TheCleaner - When I beat level 10, I started buiding Wealth, pure white, and pure blue gomphus, and mid-game I shifted to building an assortment of special-effect gomphus. An assortment is needed to deal with the various immunities. I use a mixture of Splash Slow, Instant Death, Stun, Plant Bomb, Confuse, and Teleport. And some enemies will get through anyway, so you need Life Steal to top off your health after they escape.
Daikaju - Mid-game, I shift from buiding Wealth, pure white, and pure blue gomphus, and start building an assortment of special-effect gomphus. An assortment is needed to deal with the various immunities. I use a mixture of Splash Slow, Instant Death, Stun, Plant Bomb, Confuse, and Teleport. And some enemies will get through anyway, so you need Life Steal to top off your health after they escape.
Ditto what BornIn1960 said. One of my big breakthroughs was realizing how important Wealth (red,yellow) gomphus are, especially early in the game. Manage your damage-oriented gomphus to weaken the enemies so the Wealth gomphus can kill them.
clairebear - The guide at the URL in the game description above is pretty good. The big breakthroughs for me were discovering the upgrades (and going back to earn gold medals at earlier levels to get more points for upgrades) and realizing that Wealth (red, yellow) gomphus are important, because they provide the $$$ to build/upgrade the other gomphus that you'll need.