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 ;)