Perfect Composition (HARD) Clear Onslaught with all 5 people playing as the same character
Space Wizards' Guild (HARD) Clear Onslaught with all 5 people playing as either Ziggs or Sona
Morning Star Veterans (HARD) Clear Onslaught as a team without Sona or Ziggs, and only 1 Jinx
Planetary Legends (HARD) Clear Onslaught with each person having 4 or fewer Augments equipped
Galactic Legends (VERY HARD) Clear Onslaught with each person having 3 or fewer Augments equipped
Universal Legends (INSANE) Clear Onslaught with each person having 2 or fewer Augments equipped
I think you got to the root of the problem with this event in a way that did not occur to me. I don't think it unreasonable to expect and event to be entertaining and fun. Looking at the later quests in the extraction line, however, it seems like they were designed with the opposite intent in mind: to frustrate players who try to complete them into abandoning the quest line. With this being a limited time event and all, I think it would be in everyone's best interest if they loosened the restrictions on this missions and just let them be fun.
For example, remove the Onslaught requirement and make it so only you need to have the required number of augments equipped. I don't mean make every quest doable on intro, that would not be any challenge. They could do something like
Perfect Composition Clear Cadet or higher with all 5 people playing as the same character
Space Wizards' Guild Clear Cadet or higher with all 5 people playing as either Ziggs or Sona
Morning Star Veterans Clear Cadet or higher as a team without Sona or Ziggs, and only 1 Jinx
Planetary Legends Clear Captain or higher with you having 4 or fewer Augments equipped
Galactic Legends Clear Crewmember or higher with you having 3 or fewer Augments equipped
Universal Legends Clear Crewmember or higher with you having 2 or fewer Augments equipped
This would give some challenge to the quests while enabling the players some flexibility in the difficulty level, and offer them the option of completing multiple quests in one game without inconveniencing other players with requests for everyone to drop their number of augments. Above all, it would inject fun into the later quests of the event. Here, for example, are the missions for the upcoming Killing Floor 2 Halloween event https://steamcommunity.com/sharedfiles/filedetails/?id=1510591602. While things like kill 25 zeds with traps would take some effort (and looks to me like the hardest of the bunch, given how unreliable trap damage can be), it still appears to be a fun challenge for the players to complete. The same goes for the 25 wave endless and defeat Hans on hard or higher (the difficulties of KF2, for those who never played, being normal, hard, suicidal and hell on earth) gives flexibility to the players while preserving the challenge of the mission.