"As a team take down 3 dragons"
I assume it means 3 drakes, and it seems "as a team" they mean all 5 members must be attacking the drake? I've not been able to get that to happen so far even in bots. I've asked around in game and no one I've spoken with has figured out how to get any progression on this mission. There's no specification on wether this is strictly a pvp mission or not.
And if this mission does require you to get all 5 team members together to kill the drake 3 times, I feel that is poor design. As it relies entirely on the luck and chance of getting 4 other randoms to cooperate with you, and it already feels like no one listens to anyone anymore. I can't even get a team in co op vs bots to stop what they're doing and come for drake.
Just had a bot game where everyone agreed to and joined up at drake. We took 3 separate drakes all together, with all our icons showing up on the pop up when drake dies. None of us got any progress. Our Master Yi said he'd report it to riot. So even with entire team together it doesn't seem to work.