The lights are on
1) Take cover. Got it? This is Insanity, and your enemies have ridiculously accurate aim. You're Shepard, not Rambo. You died once, and you can die again.
2) Always have atleast one character with the Warp ability or Overload in your party. Everything comes equipped with shields in Insanity, even Varren, and one of the fundamental rules of surviving this mode requires that you to be able to weaken them quickly.
3) Always make sure you place your characters in secure locations in tight firefights. Y'know, so they don't go running off into the middle of a firefight and die (hmm, Kasumi, Tali, or Jacob, anyone?).
4) If quantity doesn't always equal quality, the reverse can also be true. Heavy weapons like the Arc Projector, Avalanche, and that wonderful Flamethrower are worth their weight in credits. The Arc Projector can do considerable damage to large groups of enemies; the Avalanche is useful for freezing them - once their shields have been destroyed, of course - and the Flamethrower is awesome for enemies that like to get too close, vis a vis Husks, Abominations, soldiers, mechs, and Varren. The Cain is also great, but it's a meh when you're not fighting tough bosses, especially seeing you have to have atleast 100% ammo to use it.
5) In high-powered action movies, is the explosive tank of gas ever sitting next to an enemy just for show? Take advantage of your environment in battle.
6) Sun Tzu once said that the enemy with the high-ground always has the advantage. Not in this game, when you can curve biotic abilities to tear them to shreds. Or sniper rifles...
7) The one-two punch: destroy a husk's shields with Heavy Warp - or just whittle it down to its health - and then use Incinerate to instantly kill it.
8)Don't use Unity too often when both squadmates die in your party: this will automatically use up two of your medkits instead of one. Instead, pick off your enemies with your best weaponry. Your characters will revive themselves once you've picked off all the enemies. If you absolutely must, then use Unity once you've killed enemies around them. But otherwise, exempting battles with enemies that like to flank, don't waste your time, as you can and probably will survive by yourself in most cases.
9) When using SMG's and Assault Rifles, fire in short, controlled bursts to minimize missed shots.
10) Evolve atleast one ammo ability so that it can be used by the entire squad. While it may seem tempting to have that +60% damage for one character, three people with special ammo and +40% damage is certainly much more devastating. In this case, less is more. Especially Warp ammo, easily my favorite of the ammo abilities as it uses biotic power to damage shields and both synthetic and organics equally.
Here's the cous de gras: when choosing your special ability, I recommend one that either optimizes your defense (Fortification, Shield Boost, Barrier, Cloak) or your offense (an ammo ability or a grenade ability) based on your class. It's best to use Fortification for a Soldier class since they don't have any good defensive abilities.
11) For squadmates like Jacob who die frequently, evolve their passive abilities first.