This is a very strange thread. I see what you've done here:
1.Stacking impossible odds
a) claiming that only Superman can defeat Mandrakk because, well, he is Superman. Duh. If only that could be a joke....
b) saying that all the plot devices that were used for the victory by Superman are unaccessible to Thanos
2. Depriving Thanos of any advantages
a) dropping him in an unknown to him universe
b) giving him what - 1 week prep?
c) forbidding him to bring over any artifacts from MU
3. Baiting like hell, and gleefully so.
Some good fellows you are, huh.
Anyway, there are still ways.
1) Time-travel allows Thanos to travel in any time and , therefore, gather almost all the information needed. Like Miracle Machine.
2) But he won't need it. The only thing he would need here is Imperfect Duplicate Ray, vs. 2, that can work on Mandrakk. Imperfect Duplicate of Mandrakk will save the stories of DCU and be the embodiment of concept of good.... or something just as convoluted and meta. Mandrakk, out of equatation.
3) ALE won't work on Thanos just because. Did it work on Batman or Superman? Let's say for the same reasons.
4) Thanos doesn't really care, so he would just shatter time-space to the point of Darkseid hanging on it is no longer possible, and stone-face with howling falls further into abyss
5) When Mandrakk arrives in whatever remains of DCU, Thanos wishes for the happy endinf... for himself. They he just watches how DCU dies through the infinity Well, turning away only to kiss Death one more time.
FC: owned, Thanos: wins