I've noticed a bug/exploit related to the pause feature of the game and the battle simulator: You're only supposed to be able to fight in the simulator every 60 seconds, but if you click the settings button to pause the game, the simulator recharging clock continues to count down. Therefore, you can continue to advance your level from the simulator without advancing your game day.
For most levels, a combination of machine gunners and missile launchers were sufficient. For the 8th level, I'm not sure how you can do it 3 star without the mortars. I put a mortar in the middle on both the left side and right side to support gunners and launchers - they can decently take out wheeled vehicles and will flatten a large group of running soldiers. It's also worth pointing out that the more expensive "anti-tank" missile launchers do not attack infantry. This makes them less useful on most stages since their fire rate is slow to begin with.
For those struggling to get the achievement for looking at the instruction page, you need to start a battle and then click on the grey ? once you're inside the battle pane.
My strategy for killing the Colossus was to do a tactical retreat. Units were all ranged attackers (Centaurs a must) plus the goblins. All units had Platinum Swords. Fight all the way down to the Colossus and get it to start moving. Use the goblins rage to boost your ranged attacks, and send the goblins to die at the Colossus. When the Colossus gets close to your ranged fighters, retreat everything about the length of one screen and then send the goblins alone to attack again. Every 60 seconds redo Rage. Every time the Colossus gets close to the ranged, retreat them another screen-length. At a certain point if you've spread out your goblin deaths enough you will get to a stasis location where goblins are arriving as fast as they are killed and the ranged units can just sit and attack. Centaurs will kill anything coming behind the Colossus like apes and enemy goblins.
For those struggling with Level 13, the "Raining Goblin" stage, make sure you include Orangs and Popo the Dwarf. Early on you will want to hit the castle with everything you have. When you see a black goblin that resists all attacks, back up everything to about the middle of the screen. There are two tall trees in the background around this point - line up your forces at the first tree and continue to keep readjusting them so that they don't get aggro'd to attack the black goblin. Eventually Popo and the Orangs will do enough ranged damage to destroy the castle. The more you've powered up your guys the faster this will go, but it can take 30 mins or more if you haven't invested any upgrade points.
Twinlights - you probably got your boost key stuck. Try tapping it (it's one of zxcvbnm) at the start of a round. It's similar to other games where left or right can get stuck, and I've heard is an artifact of something to do with Kongregate chat.