I have been wondering this also. I just use surge storm dash and that seems to complete the task. 

Hello! You mustn't be attacked to complete this Task. You can be attacked after the strike is completed.

@CrystalDrew: Thank you for your answer, but then this is not in line with my experience; see point 3: "I had a 5x5 game in which I killed 6 or 7 mechs in the first round without being hit at all; but I was hit in the second round. The task did not complete. " 

I imaging that by "attacked" you really mean "taking damage"; for instance: 

• being shot at, but dodging and eventually taking no damage does not count, right?
• taking a hit that is completly absorbed by a shield does not count, right?

If you take even the smallest hit from a stray bullet or fragment, it counts as taking damage and you won't complete the task. 

I was very careful yesterday, and indeed, it looks like you have to make the 4 kills before being hit the first time. Maybe that in the case 3) of my first post, I had been soo marginally hit that it was not visible on my HP bar. Anyway, thank for your answer.