G.I. Joe: The Rise of Cobra

I'd recommend going for this outside of your campaign completion by returning to the Arctic missions, setting the difficulty on Casual and replaying the very first level of the game (with Duke and Scarlett). This way, you don't have to worry about getting a low score and it avoids the problems I had in the higher levels due to the wonky targeting system and multiple targets -- where I'd think I was aiming at a turret, but I'd tag a trooper who just dropped in front of me instead.

In the first level on Casual you can actually run right by all the troopers - you don't need to stop and fight a single one to complete the level, so just give one or two of them a swift punch and a kick as you're dashing by and that'll be enough to count as "only using melee attacks on ground troops" (following this method will give you a really low score though, which is why I recommend doing it as a replay).

The only things you need to shoot in this level are the gate turrets in Checkpoint 1, the generators in Checkpoint 2 and the HISS tank in Checkpoint 3. Just make sure to position yourself to take these out with getting any troopers in your crossfire (there'll only be 1 or 2 troopers around the turrets and generators, so it's fairly easy).

I would also advise that you do NOT enable the Accelerator Suit when you are given the prompt to do so (during Checkpoint 2), lest you get carried away with the power and start blasting everything in sight, including troopers. Instead, save it for when you have to take out the tank and it'll make that battle go by a lot quicker. Once you've done that, the level should end and your achievement should pop.

ALSO, if you haven't got the "Sloppy Joe" achievement yet, then you could probably unlock it here as well (which is what I did), so long as you don't "die" during the level and follow what I mentioned here as well as the tips Boramir1 put in his guide for that achievement.