Considering the game of innovation (see, eg, https://boardgamearena.com/gamepanel?game=innovation) a 2-player game ends on 6 achievements.
Usually an achievement takes an action to complete, but special achievements occur when a condition is met.
Therefore, it is possible to end the game with more then 6 achievements, if the last 2 (or more) where special achievements. For example, you can have the empire achievement and the universe achievement met with a single meld.
I am trying to come up with a way to do the 5 achievements at once.
For 4 achievements, we can have empiricism causing a splay (if the last unsplayed color, wonder achievement) with the melding of an ten (if the last color with card < 8, universe) that might reveal clocks (world achievement) and other symbols (that might be sufficient for the empire achievement).
(for the purposes of this question, let's exclude expansions. I will ask another question for expansions if no solution can be found)