I remember doing some research before going for that achievement myself, and yes, you do need to be on Death March from the very beginning to the very end (of the main story).
NG+ on DM should unlock the trophy though. I dug around some and found people saying they got the trophy/achievement on a NG+ save.
NG+ on DM can be really, really brutal (unless you have a super strong build that just mows down all enemies). DM without NG+ also gets really brutal at higher levels, again unless your Geralt is super powerful.
If you don't mind playing through the game more than once I'd say it's better to just continue with your current save. That will allow you to turn down the difficulty if a fight seems impossibly difficult without needing to worry about the achievement. Knowing what to expect would make a second playthrough, NG+ or not, that much easier.