If you're looking at how best to get this achievement, you'll have completed Hardcore mode already, and played through the entire campaign a few times already, so you should be as familiar as you can be with the game, how it works, how best to play it, etc.
With the Insanity difficulty, the difficulty gets ramped up a few notches from Hardcore, but susprisingly isn't as hard as you'd expect. The main thing you'll notice is how much health all the enemies seem to have, especially the Thorian Creepers. Killing becomes more of a feat of endurance, and thus survivability.
If you plan to start from scratch, check out some of the great guides to doing so. I advise against it - starting with an old character in the high 50s will help you steamroller your way through the campaign in around 5-6 hours without the need to struggle through sidequests to level up, and in even unlocking this difficulty (and the ally achievements) you should be near enough level 60.
I used a few simple tactics to minimise time, and efficiency in missions, to get right through as quickly as possible, and did this in 4h 58m. I died twice in total, and never in the boss battles - and believe me, I'm not great at this game at all!
Save often, and on numerous slots. If you do happen to die, or mess up somehow, it'll save you time and effort. Naturally, you can't save whilst there are enemies present, but there are a few tricks to this that'll come in handy.
-If the save option in the menu is greyed out, and there are no enemies around or on your radar, wait a few seconds before trying again. Your allies will holster their weapons when it's safe to do so.
-If you're in the Mako and enemies are on the radar but not nearby, then get out of it! Your radar on foot is minimal compared to the Mako's, and chances are the red dots will disappear, allowing you to save. This is particularly useful on Virmire and Noveria.
I took my level 58 soldier (who hadn't done the bonus specialisation mission due to laziness), and maxed out everything except handguns, snipers, and shotguns. I used the assault rifle you can buy in the Normandy, with two frictionless materials and plutonium ammunition. This means you'll poison the enemies, and the gun will never overheat, so you can keep your finger on the trigger throughout battles... If you're not playing as a soldier - don't worry. Your teammates will be doing most of the work anyway, and as long as you can deal damage and stay alive you'll be fine. Armour wise, I had decent heavy armour on everyone. Not the best (because I couldn't find it anywhere...), but it worked just fine, so if you can't find any Colossus armour, don't worry.
For squadmates, it's by far the best to take Wrex and Ashley, and max out shotguns and armour abilities. Ignore other weapons completely and use the points you'll save in health etc. I'll explain this in the next section.
Some people seem to want balanced squads in this playthrough, but to be honest you really don't need any technical abilities whatsoever. You have no need to decrypt anything at any point. Biotic abilties can help, I guess, but at the expense of a shotgun... which I'm sure is a better option.
Double Shotgun Tactic
Informatively titled, this is the one tactic that made this playthough an absolute breeze. Equip both of your squadmates with the HMWSG X shotgun you buy on the Normandy, with two Scram Rail Xs and High Explosive Rounds X. These guns are absurd, and whilst they don't do a huge amount of damage over time, they fire enemies up into the air, against walls, etc, which stops them attacking you! Geth Armatures are the only things that'll be unaffected, but in the rare battles with them find cover, popping out to chip away at their health bit by bit.
With this tactic, you're free to keep up a stream of bullets whilst your allies act as crowd control. Use invulnerability as often as possible, and adrenaline rush if you need to use it sooner than that. It's as simple as that really. Overkill too if you want, but I couldn't be bothered most of the time and it didn't affect things really. Keep an eye on what guns your allies are using too - they have a weird habit of changing to a handgun after some cutscenes, which really won't help saving the galaxy.
A quick note with this tactic - the game seems to get confused sometimes with the enemies flying through the air so often, and occasionally they'll get stuck in walls or in uncreachable areas, stopping you progressing. This happened to me in Chora's Den right at the start, where I had to reload the autosave when an enemy appeared on my radar but in a wall somewhere, meaning I couldn't kill him. It happened again in the Thorian's Lair, but a reload of a save did the trick again. Weird, but only slightly annoying in the grand scheme of things.
Possibly the hardest bits of the game will take place in the Mako. As other guides have said, your best bet is to plough straight through your enemies. Try to run over Armatures and Colossi - this'll stop them shooting you, and go straight to the destination.
If the Mako starts taking a lot of damage, try to get away from enemies and jump out, using the save trick mentioned above. Then, reload your game. The Mako will be back to full shields, and you can continue your journey. There wasn't a point in the entire game that I couldn't stop the Mako in a peaceful site somewhere en-route to wherever, since the Geth tend to be spread out in batches.
A note about the Krogan. They're easily the most difficult enemy in the game, but if you stick to the gameplan they're not too bad. Keep invulnerability up, and stick close to your allies. They take a few shots to get launched into the air, and usually take a few downings before they'll die. There was a point on the Citadel at the end with five or six of these at once, which I somehow scraped through. If you stick by your teammates and keep the bullets flowing, you'll be okay.
For the record, I was an evil b*****d throughout this, to speed things up. Being good seems to take a little longer. Holding the analogue stick to the bottom right and hammering X repeatedly gets you through the dialogue with gusto! Unfortunately, the cutscenes are unskippable, and I'll be seeing that vision from the beacon in my sleep soon, I've seen it so many times.
Put your difficulty to casual and blast right through. Before clicking on the beacon, change the difficulty to Insanity. If it's not there, you haven't played through Hardcore yet...
Your first taste of just how much health the enemies have. Ignore all side quests, just nail through the quests. The enemies should pose no problems; send your allies roaming around the rooms and watch your opponents fly everywhere whilst gunning them down slowly.
Liara's Dig Site
Use the Mako tactics listed earlier. Ignore enemies, drive over as many as you feel like. Once you get on foot it's relatively simple. Go slowly where necessary, remember to keep using invulnerability. The mini-boss battle at the end shouldn't cause any problems either.
Get inside, speak to the Hanar merchant, agree to smuggle for him, grab the package from the dock, then give it to the administrator to get the garage pass with no fighting required. Usual tactics for the Mako section. Once you get to the Rift Station and deal with the Rachni (which aren't difficult at all) go to the medlab, agree to make a cure, then head to the Quarantine Labs to do so. Back to the doctor, and he'll give you a pass to the Maintenance Bay, cutting out even more fighting and letting you straight to Benezia.
Some say she's the hardest boss in the game, but I wouldn't worry too much. At the start of the battle head right and run to the corner there - this'll stop Benezia attacking you. Hang around this corner as much as possible in the first section and it'll be easy. For the second part use invulnerability straight off, then hang around your teammates, who should be launching various Asari soldiers into the air. Focus on Benezia, then her minions, and with any luck this'll be done with in no time.
Once you clear out the tower at the start and talk to Fei Dan, ignore any side quests and get in the elevator to the skyway. Ignore everything in the Mako, including the outpost the game wants you to stop at, except on the way back where you're forced to. I didn't bother saving any survivors (too much hastle messing with grenades). You'll notice how absurd the Creepers' healthbars are, and it's simply a matter of patience killing them. The shotguns come into their own in this section. The boss is more of the same. Go slowly, saving where you can, and grind your way around the Thorian's limbs. Kill the Asari first, since their biotic powers mess up your rythym! You've ruined the colony, well done. Move on.
The Mako section can be difficult, and I needed to save and reload a few times to keep the shields fully intact. Otherwise, same rules as usual apply. Once at the camp, make sure you don't stupidly kill Wrex (now is a good time to be careful with dialogue selection!), and make sure Kaidan goes off with the doomed Salarian team. It's business as usual again from here. Once Ashley stays to arm the bomb, choose a new squadmate you like (I chose Liara for her biotics), but don't bother giving them the shotgun if they're untrained for it. When prompted, leave Kaidan to die. Ashley has the great shotgun in any case! For Saren, keep your fire on him, and shoot the fuel tanks he likes to hover over. He's probably the easiest boss in the game.
No enemies - no problems. I punched the reporter for much lols.
Substantial numbers of Geth Destroyers and Juggernauts can be problematic, as can the Armatures at the start. Go slowly, use invulnerabilty, and chip away from cover. The Mako section should be easy after Virmire's.
The hardest normal battles of the game. Go slowly but methodically down the long corridors. For the open area with the dropship sprint to the turret you can activate, then retreat back safefy while it's health slowly goes down. The area with Geth turrets can be tricky, but doesn't require any special tactics.
For the final battle, go hide behind the concrete pillar (without this brilliant piece of architecture this battle would be near-impossible), and use overkill on him. Keep an eye on your health and use invulnerability (as usual!), and he'll go down with relative ease considering he's the last boss. Halfway through he regenerates his shields and speeds up a bit, but the battle strategy is no different to before.
And there you have it! The galaxy has been saved on the hardest difficulty going, thanks to one man and his shotgun-weilding gang. Any questions, post them in the comments and I'll get back to you. And if I've forgotten anything, let me know. This is all from memory y'know...!