For future game modes with achievements/missions like this please add an exclusive 5 premade only mode and keep these out of blind pick.
I've got the 4 augments and done a 5 ziggs run with one being a premade team and the other with random people.
I was able to get some of these team specific achievements done no problem but in most of my games it was hell because people are always fighting each other over who we should pick and our set ups and if one dickhead on the team doesn't like our set up they will intentionally troll/rage quit/afk/flame all game.
Also as a bonus for all game modes can you give a whole week suspension to trolls or rage quitters (not people who are having connection issues) or cry baby flamers who ruin these game modes and just like the denial of ranked features, shut out all rewards and missions to these toxic players.
You should allow all rewards to be available to positive players as this will cause more people to think twice before posting a flame comment, or troll the team in anyway.