The fastest way to gain experience depends on what you're best at.
For instance, if you can consistently place close to the top of the leaderboards in a multiplayer game mode, that's probably going to provide the best experience gains per unit time spent. Don't play a free-for-all game type if you're more of a team player, and vice versa.
Likewise, if you're terrible at multiplayer, you're almost certainly going to get better experience bonuses from Spartan Ops. If you're going to play Spartan Ops for XP, go for the Matchmaking version. You can only play the current episode (for now, at least) and you must play Heroic. However, episodes go by quite fast, there's no friendly fire, and you'll tend to end up with ~4-6k experience per op. I find this to trump any XP per time invested in any other mode. If you've got double XP tokens, this is the place to use them.
When it comes to "War Games" style multiplayer matchmaking, I find personally that the "unusual" team game types tend to net me more experience. Anything with a Wraith, a Warthog (if I have a good teammate), or an abundance of power weapons and I'll do well. If you don't play with a coordinated party, these might not be the best for you. I have friends who insist that team slayer is the fastest way (or SWAT, whenever that becomes a playlist...). For me, though, I'll lose a BR or DMR fight often enough that I tend to end up with a K/D of less than 1.
Do note that you'll gain an good chunk of experience just for finishing out a round in online matchmaking, so don't quit early if you can avoid it, even if the game is going poorly. This bonus is by design, to give incentives to people for not quitting early.
Another thing to pay attention to is the periodic challenges. You can see these by pressing Start on most of the menu screens (this menu is called the "Spartan Hub"). Select the Career pane, and then the Challenges button. There's big bonuses on offer for varying time periods in various game modes.
Keep these in mind when you're deciding what to play - the playlist and difficulty matter for some, but for others you can set the game to easy and play on a level/game type you know well and walk away with a sizeable gain in a short amount of time. Whenever I start to play, I'll check out these challenges and try to knock out the fast ones before I do whatever I'm really planning to do.
without one preventable Marine death
Try the mission on easy, you should be able to save everyone.
Except those that die because they are scripted to.
Those scripted to die will always do so under the excact same circumstances, even on higher difficulty.
Also, here's a video guide: Link
Best Answer
"Core" is Episode 1: Chapter 5. Note that the achievement specifies Chapter 5: Episode 1.
This is made doubly confusing by the fact that they put the chapter number first, even though chapters are a subset of episodes. All of the other Spartan Op episode/chapter achievements do this as well.
Therefore, you can't get this achievement by playing the Spartan Op "Core" - it is for a Spartan Op that has yet to be released.