I found the most effective game type was Rumble. You can post up, and not draw attention to yourself because there is no centralized objective. Sure its cheap, but effective. even if you just get about 2-3 kills a life, thems gainz.

Heh, yeah it was really tough. But if at all possible I'd argue that you try the "regular" way as long as possible. Because when you finally make it, it's such a huge feeling of accomplishment. Plus the questline in general is a pretty fun one, just that first step is a doozy.

What I ended up doing.

Played control. this let me have defined spots to snipe, super, heavy at.

Sniped until I ran out of ammo, switched the last word off to whatever you are most comfortable with. Once I picked up special ammo I would go back to the last word.

If I saw people coming at me while I was sniping I just ran away. keeping people at distance was my friend.

If I had a super or heavy then I made sure to still play conservatively and let people run into my insta-kills.

never be the aggressor and play ultra defensively.

If you are playing a match where you are just getting killed, frustrated, jumping off maps, etc... then use a different weapon. Only play on maps you are comfortable with.

went on a 15 kill streak and just demolished

This quest line can go screw itself. It's 5:30am here, I keep waffling back and forth between 25 and 50% in Tex rep... I just want my shotgun.

I'm going to resort to the cheesing method of unequipping and reequipping, grabbing heavy, hiding until my super is up and then blasting the SOBs to kingdom come. Can't wait to clear this step >.<

Hop into Salvage with a team, and have them point out enemies for you, or let them soften them up for you. Assists or Kills, it helps, and it's easier to stay alive. Also, whether you're capturing or disabling, you're PTFO, so there's more points there.
Sammy had the whole thing done quickly this way after making slow progress through the other playlists.

In this video, Chaos and I started letting her get most (except for a few, heh) of the kills:

I did it in Rift. Rather than playing to get the rift, I played to flank those on the other team trying to get it. In addition, I'd swap it out so I'd not be using TLW until I had heavy, super, or 3 kills in a row already, making the likelihood of a multikill or streak medal much higher while minimizing losses. Always swap to TLW when the game is near ending if you're gonna win - that's a 3% bonus.

I hid, I cowered in corners, I played with different weapons to build up to a streak... but it's done! This next shotgun step is super easy, which I appreciate. The NEXT part will suck, though. I hear that strike is a massive pain.

Grabbed a random or two off of the /r/fireteams subreddit, ran the strike and made it all the way to Charmander and Blastoise without any problems, but damn, those Psions are a massive pain in the ass without Void weapons. Void heavy too too long, so imagine my delight and surprise when I found my 300-level Arc shotgun still one-shotted the little bastards!

Clear the adds, smack the bosses, two attempts and we're done. Now all I need to do is wait for Tuesday... and on Wednesday, I get to finish my Exotic Solar sword quests. Frying pan -> fire.