Halo 4

The best way to do this achievement, for those who don't want a tiresome grind on the same map, is to aim to complete the challenges found in your Spartan hub (this commonly starts on your loadout's and name etc so flick up on LS). Here you can see your progress towards challenges and offer huge amounts of XP. There are challenges for the campaign/multiplayer and the spartan ops, so mix and match. You will eventually reach this in time so keep going

Play spartan ops on easy, gets you 2k or more a game
Found the 2nd mission in Ep 1 is the shortest one.

But the same mission over and over can get boring so bring a friend.

Edit. you dont have2play the same mission over and over ch 1,2,3,5 get u nice xp ch 4 gets you a tad less.
ch 1,2 are fast and the rest are easy but take tad more time.

Also by doing the same mission over and over you keep working on the same commendations and at the higher levels their worth a nice amount of XP :)

As others have mentioned, doing the challenges across all modes will help you level faster. Don't forget you can use the DewXP.com program to get double XP. I think it's kind of silly to spend money on the codes (people are selling them on eBay and such), but if you're going to buy Mountain Dew or Doritos anyways, don't forget to use the codes. It's not much effort (or at least, you can sell them and make some money off of them, lol).

What I really wanted to say though, is that grinding the Spartan Ops missions seems really boring. If you don't want to play multiplayer, and you don't mind waiting, why not just wait and play the new Spartan Ops episodes as they are released? You're going to play them anyway, so don't bore yourself by grinding the missions now. Wait until you've finished all five episodes (one is released each week). Then if you still haven't reached SR-20, at least you'll have much less grinding to do.

Also, even if you're not very good at multiplayer, it won't take long to rank up to SR-20. Most of your XP comes from simply completing a match. Your individual score and potential victory bonus gives you a much smaller amount of XP than the completion score.

If you worry about your multiplayer skill, stick to Big Team Infinity Slayer, Dominion, and CTF. Don't rush into battles, but rather, engage opponents that are already being engaged by one or more of your teammates. Hang around the edges of the battles rather than the front. It will be good practice and you'll get better. You can help your team with the objectives too. Don't rush into battle, and especially do not take power weapons and vehicles and rush into battle alone. It won't take you long to rank up to SR-20 and it will be more fun than grinding a Spartan Ops mission over and over.

If you want the most points the fastest do Episode 1 Chapter 1. Hop into the Gauss Rifle Warthog as the driver. AI drivers are terrible, but crazy accurate on the turret. Hopefully a Rocket Gunner will take shotgun seat, it helps. Stay in the Warthog the whole time. There's tons of Wraiths, Phantoms, Ghosts, and Elites. If you kill everyone and only one of the Phantoms you get around 2300XP. So if you can take out more thats great. Can be done in around 10 minutes.

Download halo waypoint and boot it up then watch this - https://www.youtube.com/watch?annotation_id=annotation_27500... (not made by me) and input the codes, boot up halo 4 and complete one spartan op (make sure to do a challenge to get some xp in this mission) and you'll get the achievement when it says mission complete.