So, I think the Kill 40 players quest is an odd one. The kill 20 players or 20 of a certain class work with group kills.
Not 100% sure on the 40 players one. But it does seem a bit buggy within a group. I know the kill 20 ones will count even if you didn't damage the other player but your group killed them and you are close by. But the 40 will not work that way. The 40 one is definitely better to do solo, where all you need to do at that point is do damage to an enemy and be close to them when they die for it to count.
Topic. Sounds easy, doesn't seem to be So...1 vs 1 sure....you kill um and ya makes sense. However.....over the weekend I played my healer in a group, which is a lot of fun. I recall blasting crystals into mobs...I know I targeted and assisted at least in killing several...but my quest of kill 40 players never went past 0. So...what constitutes a kill...100% damage? 50%?