You can claim this achievement if you are eligible for the Meet-up achievement, and the meetup connects previously unconnected groups of at least two people each (see Meetup graph). If several meetups accomplish the same connection on the same day, all of them count.
Connecting just yourself to a group or another single person which is not member of a group yet to your group wouldn't count. It will give the newcomer the meetup achievement anyway, since this only can happen if it's someone's first meetup in any case.
It may also happen that not everyone participating in the connecting meetup contributes to the connection - namely if it's a meetup of at least three, where one (A) is a first-time meetupper and the other two (B and C) members of unconnected groups. However, since that results in an indirect connection between B and C via A at the same time B and C are connected directly, A could get the achievement too. Kind of a bonus for attending larger meetups as your first.
This achievement is awarded due to changes to the way the graph appears on the page, not due to actual order of meetups. If you connected two huge groups years ago, but it only gets added to the graph today, after the groups have been connected by someone else: bad luck. Otherwise, there would be ugly un-awarding edits.
It is not yet clear whether this achievement can be awarded retroactively, which would have to be based on the history of the Meetup Graph page.
A scoring based on the size of the smaller group has been proposed.