Stips:
-Peak Takion.
-All participants are fully healed between Rounds.
-Fight takes place on New Genesis (all powers are fully functional, obviously.)
How far does Takion get?
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"I am tired of Earth. These people.
I am tired of being caught in the tangle of their lives."
It boils down to whether his Source powers are extended into MU. Since the source is basically the source of everything (Speed force, quantum field, CPB) Takion could basically manipulate any powered being however he likes. If we allow this ability to be extended into MU and assume he can manipulate the power cosmic for instance, then there's no reason for him to lose.
Worth noting that even Spectre was completely overwhelmed/owned by the energy of the Source/Godwave, and literally unable to do anything against it: http://i.imgur.com/MH0wFdT.jpg
didn't darkseid stop the godwave when Ares was in possession of it before (or something like that)? Anyway, with all of this information brought to my attention, I'd say that his first real challenge would be around the third round (assuming that the team sinergizes properly). I think that he probably stops at the fifth fight.