OK, finally worked out what was going wrong. I had all upgrades and tried the last level five times following the advice of everyone in the thread, but it was never even close to doable. But, I had the game set to low quality - I had some stuff running in the background earlier in the game and wanted it faster, but at the boss I didn't have this running. When I switched the game to higher quality, it lagged a bit and the cooldowns felt like they were coming up much faster. And bingo, I finished the game with a ton of lives and the boss still quite far away.
Play Recruit. Complete single player to get shotgun for Gun Running Challenge. Use pistol whenever possible (press Q) and kill 50 to earn best pistol for Pistol Room Challenge. Get 50 headshots to earn best rifle for all other challenges. On Kosovo Sniping, kill order for those without audio: back right, back left, front left, front right, front centre. Detonate explosives with click, sometimes need to wait (presumably for audio)? Just keep clicking (secret to success for this game ;)
Did first 33 levels on hard, then 34 on easy, and ignored 35 and 36 to get 100 stars.
The key mechanism of this game is that overwhelming numbers will have a higher kill rate. If you are losing, you need to immediately reinforce or pull out. If you are winning, reinforce to make it quicker.
For people having trouble at the beginning on hard, here's how the mechanism works: It is cheap to attack neutral planets and expensive to attack enemy planets. Your goal is simply to get a higher population than your opponent then defend every planet. It's fine to leave the slider on 100% and send all your troops wherever the enemy is attacking you. Then only attack when you are ridiculously overwhelming.
Thanks for all your advice on "put in survivors with better this or that". I have NEVER had more than one survivor. I get one, they die, I get another, they die. Never, not once, have I ever had a CHOICE of survivors.
Stimpacks add two to your current AP, e.g. if you are on 2/7 AP, and click stimpack, you will have 4/7 AP. You need at least 1 AP left to be able to select it, and on max AP it is wasted. So, use at least 2 AP and less than all your AP before using stimpack.
OK, manage to get the badge with a magic build character. What you need to do is equip the level 1 freeze, fire, and poison attacks, as well as the level 3 lightning and poison. Use the level 3 attack to clear the screen, have pet as agressive so he attacks the boss, and get behind the boss. While he's facing away, do the freeze attack. If it freezes, do the other two attacks. Repeat. Be ready to heal / recharge mana.
Be a scoundrel. Max the second skill, then start work on the third. Get every trophy then buy the money trophy upgrade first (15 trophies). Then buy XP ups. Later on you should be upgrading all equipment every 3 or 4 levels. Exit shop screen and go back in to refresh. Don't forget you can only wear equipment up to your level. Defence (on the vest) is IMPORTANT, keep it maxed all the time where possible.
Actually, slight modification - on endless, buy all skills as well as upgrading all buildings before going up an age. This is because going up an age shortens the disaster timer (a LOT) as well as adding worse disasters.
Use Gext3r's two comments' build order and advice on last tutorial, time attack, and endless, it's good. For time attack it's quicker to make two or three level one nexi. For endless it will be easiest to make one, as after a couple of levels nexus upgrade costs don't change and you therefore save on building points. Delay is required in endless, once you have production maxed and all skills you should be firing Delay every time it cools down, **irrespective of the upcoming disaster**.
The "Booster" equipment (enables First Strike) is pretty much the most ridiculously overpowered item - I had an elemental/healer Mari who had had all MAG/MP stat choices, once she had over 120MP and booster every battle is over immediately and she keeps full MP. I got it from Mercenary Defence which is quite far in, but according to wiki you might be able to get it earlier, from the Chimerae or chests.
I like to reload my weapons a lot... and sometimes press the reload button when I die, which restarts the whole level. Game designer, I don't know if you noticed, but there are several dozen other keys on most keyboard and you could use pretty much any of them.
Use space bar with all fingers of one hand. At the beginning hold the space bar and "untap" it (let go and hold again right away) whenever you get to a wall to go really fast. Try to lose the habit of always going "under" spikes - try to go over smaller ones. And keep trying.
On Insanity mode for hard badge - When you get to the lava level, there is a point where there is a red wall in front of you, and a cave that goes below and to the right of that wall. Once you have killed the ogre and other stuff here the wall will disappear, and you should take this opportunity to run run run as far to the right as possible. This is because it spawns a bazillion enemies for you. You will trigger the dragon, and die because of all the additional enemies on the screen. But when you respawn, you will be at the dragon - the last boss.