Mass Effect

Originally i wrote this solution as I was getting the achievement, I now have the achievement and there are a few things i want to point out. I noticed some confusion on this topic in the solutions so I wanted to confirm that you have until the end of Eden Prime to change the difficulty, also something that confused me is that after you beat it on veteran or normal in the options it will say that the hardcore difficulty still must be unlocked. Select it anyway and save changes.
In order to cope with the difficulty I would suggest using the infinite money glitch (the med clinic one) to get the money needed to buy all HWP spectre gear. It is NOT required to do this I just figured i would point it out as it can help loads with the difficult enemies. Whether or not you decide to use this method is up to you, however I find that putting heat sinks into the weapons makes them even more effective. This should help a lot facing the enemies. My recommendation is to keep a biotic or at least a partial one in your party at all times. Frequently it is easier to lift an enemy or throw them into oblivion or a pit rather than unloading into them for 15+ seconds. (I'm looking at you Thorian creepers). Lift and throw combos work especially well against Krogan and Geth Destroyers that charge you constantly. In addition, polonium or chemical rounds negate the Krogan's health regen for the most part. Save often and do your best to try not to get mobbed by swarms of enemies. I also was going for the Ally achievements at the same time as this one and because they require you to complete a majority of the game with the same squad members I ended up doing most of the side quests. This will net you a lot of exp for leveling although it is not required. In addition this achievement can be gotten with any class. Most people prefer soldier but I got mine with an infiltrator so it is possible. With regards to the infinite money cheat, occasionally you will lose the ability to buy back your special ammo types (polonium, incendiary, and cryo rounds), this is not too big of an issue as you will get better ones quickly just by progressing through the story.
Good luck

After starting a new game, go into the settings menu and change the difficulty to Hardcore. You must do this before landing on Eden Prime or you will not get this achievements. You should double check the settings before you land.

I did this one by starting as soon as i finished on normal,i started a new game and used my existing shepherd from the previous game,the best place to change the difficulty setting is just near the begining after you have talked to joker for the first time,you are told to go and talk to the captain in his office,this is the first oppurtunity you get to control your character,press start,go into options,the difficulty setting is at the top of the list,change up and DONT FORGET TO GO TO THE BOTTOM OF THE LIST AND 'SAVE CHANGES'otherwise it will just go back to the previous difficulty setting,i did the same thing for my play through on Insanity,the main benefit of course is that your not starting right from the begining with no skills or having to level up from 1,this makes the game much easier,hope it helps.

its easier to start with an existing shepard (your previous playthrough shep) because he still got the weapons and upgrades from your previous playthrough. especially the earlier parts will become easier, when you normally dont have any skills. furthermore, dont do any sidequests. usually good for grinding XP, now they will only set you back.

Hardcore difficulty is do-able, enemies only take longer to kill, its not that they become stronger. It helps when you have your armor and upgrades from previous playthrough.

and DO upgrade your weapons. I only did that while on Noveria, after getting stuck just before Benezia. Upgrading my weapons did really help. I was a fool then, dont make the same mistakes I did ;)

Make a new character
Mke him/her a soldier (eventually a tank character)
Use the Commando skill for extra damage (you will need this on Insanity)
Max out your Immunity and Adrenline Burst skills (makes you almost invincible)
Start a new game on Veteran (this will prepare you for the challenges ahead)
Complete EVERY Assignment, which also includes collecting things like surveys and data discs/medallions/writings
Complete all main storyline missions as needed
Some looking around may be needed to find the source of optional assignments. I suggest checking and talking in ALL cases to everyone/everything
After completing this playthrough you should easily have 9,999,999 credits
Buy all spectre weapons avaliable to you.
The Specter "X" series is best if you get to it
Spend the rest of wasted stuff making Omni-gel for MAKO fights.
You can save at most places outside of battle. If not, wait a few seconds after defeating the enemy
then try again. In MAKO exit the vehichle and then wait and try to save. Reload game if needed
to repair MAKO.
Colossus and Predator armors are your best buy as well.
Don't forget all the Medigell/Grenade upgrades also avaliable at certain merchants as well as licenses to buy armor

After you beat the game on Veteran, start a new game with the character you just completed the last game with.
You now have a tank who can take out most enemies easily while not getting hurt hardly at all.
This will work on Insanity too. Good luck!
As far as Insanity and Hardcore go, you can ignore the side quests if you want. Leveling is your
call. Just remember there are level achievements too ;D

P.S. if you stay with the same 2 characters throughout the Veteran playthrough you will also
get the Completionist Achievement as well as 2 of the squad member ones.