"First Blood" and "Sharpshooting" are pretty easy. If you can't get those, stop playing.
"What a flight" and "Pushing the limits" can be obtained by throwing at roughly a 45 degree angle, gunning it, and matching up with the javelin at a high speed. It's pretty hard to do but you only have to do it once.
"Suicide Javeler!" is very obtainable. One such method for an almost guaranteed success is angle it so it's just touching the back of his hair a bit (close to 45 degrees, but pointing more to the sky than the ground), run to the end and throw, then gun until the distance between javelin and rocket is on the way down and gets near or slightly less than 10, which is your cue to stop speeding and just coast along and then just try to casually match him up, with a slight boost right before contact. This should net about 200 each time, which 5 x 200 = 1000 so medal get.
Note you could also get "Suicide Javeler!" with three exceptionally good runs, if you basically did a "Pushing the limits" three times out of five. But it's easier to use the method above.
"Master Thrower" is near impossible though. I imagine you just have to get very lucky or it depends on your exact browser and OS or something. Angling at 45 degrees and throwing at the very end of the run consistently yields 99 point something at the very best, at least every time I've done it so far.
Very strange that so many more people have "Master Thrower" than "Suicide Javeler!"