I would suggest that you complete the game on Normal or Easy before you try the game on heroic. This is because moving through the streets of New Mombasa takes MUCH longer on heroic than normal/easy, as you would expect.
In fact, I would probably suggest that you try the game on legendary anyway - it is not too much harder than heroic - and will only take a little longer. The achievements are stackable, so it would get you an extra 100 gamerscore for a little bit more time.
You DO NOT
have to play any of the game in New Mombasa streets to get this achievement. You can simply finish the game on easy, then load up each level individually on heroic.
As other users have stated, cover is vital - do not try to rush this game. It is best to have at least one friend with you, so that they can act as a temporary spawn point.
I completed this game in legendary with one friend in a few hours, whereas we spread Halo 3 over several days on legendary.Please either comment below or send me a Personal Message if you have any comments or improvements.