Hm, I finished it as the Engineer class not too long ago and it's really, REALLY tough.
I highly recommend you complete the game first and then import the saved data over and play with that character as the higher level will go in your favour.
I also recommend having Reave as your additional power as it sucks up a lot of the enemy's sheilds/barriers/armour and considering that even the Varren have armour in the Insanity mode, this is a very helpful power.
Learning to use the Cain heavy weapon will help you with all the big/uber health bosses like the Threasher Maw and end boss as that can pretty much knock out a huge chunk out of their health. Also find and nab as many heavy weapon upgrades as possible, the Cain only works when you have 100% ammo
I also recommend doing this as either a Soldier or a Infiltrator. Soldiers have this amazing power that slows everything down so you can knock out a baddie between the eyes quicker than you can say, 'Take it off Miranda'. The Infiltrator is also great as it makes you invisible to baddies, which is something you really need to wear down their barriers. I don't recommend being an Engineer as I found it INCREDIBLY hard!
All this and remember to save lots, try not to use medi-gel as there's not that much in the game (your squad gets revived automatically when you wipe out a certain unit of baddies)and run for your life! If you get get the bosses stuck in some of the furniture, this also really helps. Nab squad mates that can wear the baddies barriers, shields or armour (in that order) and prepare to be very, very frustrated!
Hope that helps!