This is arguably the hardest and most glitchy achievement in all of Halo. Even if you think you did it right, the game finds some little thing wrong with your jump and doesn't give it to you.
My advice? Keep trying. It took me several days of trying to get it.
PS: Remember to turn off Sprint halfway through the jump.
They were given MJOLNIR because Noble Team was an Elite team, and so they were given better armor.
As for Halsey, most say that she simply assumed that Noble Team were some rival program of Ackerson's.
Run into a convenience store (or something similar), frantically ask, "what year is it???" Then when they answer, run out screaming, "IT WORKED!! IT WORKED!!"
Make vanilla pudding. Put into empty mayo jar. Eat in public.