My stategy was to pick the Timepress, Legend and Low Tech Modifiers. Time press and Legend are your go to modifiers in this DLC as they hardly affect anything so its an easy 4x. Low Tech is odd, seeing as you need those points, but believe me you don't want to give the enemies any more health or make them harder or anything like that in this mission (In the Ghen Crag mission I picked Timepress, Legend and Nightmare) as this will be hard enough. You want them weak so you can kill them fast to raise that multiplier in game.
In mission strategy:
Don't board a UFO and upgrade your jetpack when you can. This is key, I could never get close to enough points if I wasted time boarding one. Once I realised this I jumped from being no where near to the low 4 millions instanty. A fully upgraded jetpack has unlimited magnetic missiles which you can spam to start killing enemies super fast. I finished the last wave with a multiplier of 99x, ending with a score of over 5 million. You want to have a score of 750 000 or higher by the end of the last wave.
Basically it comes down to killing as fast as possible, and practice a lot, especially if you're like me and were never very good at flying in this game. At the start of most waves the UFOs come from the same spot every time, boost straight at them head on, fingers on the triggers, go for the non shielded ones if they're there, you'll damage a bunch of them, and later when you have missiles even kill one or two straight away. Hit the breaks and circle round and start following one. Try to get behind UFOs and just follow it untill it's dead, I found that once you damage a UFO it starts targeting you a lot more.
Always be firing, I didn't remove my finger from the triggers once, especially useful when you have missiles, I can't tell you how many times Id perform a manuever or turn to look at my next enemy and I'd accidently hit or kill another. Use the look button a lot (RB i think) to get your sights on the next enemy, everytime I killed someone if there was not another UFO on screen I'd hold it down and swerve around to face it (still firing remember you could hit something).
In the wave with the walkers that fire lasers these are your number 1 priority, take them out fast. Once you can board it, board the head side, it's a faster/easier take down. Make sure you get out of the way of the laster though, don't try push it too far, I died at 4.4 mill on the last walker once because I waited to long, which was really infuriating. These are the enemies that can decimate your objectives health. Don't worry too much if you lose an objective, you can still easily make it.
In the waves with the big ships and smaller faster flying enemies concentrate on the smaller ones first. These will raise your multiplier giving you more when you take out that ship. It also lets the ships spread out a bit, meaning that you'll only have the one firing on you instead of three when you go to take them out. Once everything's dead do a run on the ships taking out the turrets, if both turrets blow up the ship automatically blows up. If everything's dead except one last ship then you can just follow it for a while from a distance if you chose. Taking out the mines it drops, to slowly increase you multiplier and get some extra points. Keep and eye on your time and kill it last for big point and multiplier bonus.
All of this combined with practice and you'll get it easy. Playing it over and over you'll get an idea when what spawns and where. It's good to remember where the mines spawn in the waves they appear in as once you've killed all the UFOs if you know where they are you can mop them up and raise that multiplier quickly at the end of the round. If you are in a hairy situation fly low and around the rock formations to regain health, especially in the later waves, you might lose some multiplier but it's vastly preferable from dieing and starting again.
Goodluck!
Edit: RadiantViper's comment has some extra helpful information I didn't put in my original post. Here it is for ease of use:
"Just thought I'd mention, the wave with the Archon you should go for first is wave 5, and wave 7 has the 3 battleships (where you can let the last one live and kill some mines for extra points/multipliers). Wave 10 also has 3 Archons, but I found I could kill all the small ships first and still have time to take them out.
I actually died literally right after I killed the last Archon (boosted right into the plateau lol), but it still went to the 'mission complete' screen and I got the achievements :D"