First of all: Katakuri has some advantage against everyone in this gauntlet:
+ Speed
+ Physics
+ Pre-Cog
+ Intang
That makes it nearly impossible for Akatsuki to beat him. But let´s start:
Round 1: Hidan
Hidan can´t harm Katakuri, and Katakuri wouldn´t risk that he do that. Hidan get blitzed with neg. diff.
Round 2: Sasori
Sasori his poison is a problem, when he could hit Katakuri. But even "when", Katakuri can see it before, so Sasori get trashed as well with neg. diff.
Round 3: Konan
Ends like round 1 +2. Without prep Konan is complete in disadvantage. (Even with prep, i doubt it would be enough for a Low Diff.)
Round 4: Deidara
Someone who could destroy something that works on Katakuri his aggregate state. Deidara can kill Katakuri, but Kata is too fast. Deidara get blitzed.
Round 5: Kakuzu
Some elements should be effect even his DF abilities like lightning, fire or wind. Kakuzu has experience on battles, but i don´t see him handle Katakuri, who should be still superior.
Round 6: Kisame
Very dangerous for someone who eats a DF, and Kisame isn´t weak. But it isn´t enough to keep up with Katakuri. He can´t even absorb his chakra, since he doesn´t have one.
Round 7: Itachi (not Edo, but Healthy)
Either Itachi wins if he uses Tsukuyomi, Amaterasu, or his Totsuka Blade, or Kata blitzes before that happend. I would say Kata is fast enough to dodge Amaterasu, especially since he can see in the future. It realy depends how the battle starts. If are both in character, then Itachi would activate Gen-Jutsu as fast as he can, but Katakuri wouldn´t attack without reaction of his opponent. So Itachi wins under this conditions. If one or both bloodlustet, then Katakuri blitzes Itachi.
Round 8: Pain (the Pain that fought Jiraiya/Naruto)
That is a though one, even for Katakuri. Of course, he is faster, stronger, etc. He has a lot of advantages, but as longe he doesn´t kill the right body, Pain will resurect those bodies again and again. They spam some animals, or try to suck his sould. Since i doubt Katakuri has soul resistance, he has a big problem here, Lucky for him that he should be far faster then Pain, so he could blitze them, before one of all of them react. He should be still carefully if Tendo activate Chibaku Tensei, since i doubt he could espace it. I will going with Katakuri this match in a mid. diff. since he can´t suprise them when they don´t have a blind spot.
Round 9: Obito (pre-Ten Tails Obito)
That is nasty, since Obito should be fast enough to escape Katakuri his attacks and he also can suck Katakuri in his world which ends in a victory via BFR. But that´s all what this kind of Obito can do. It could go either way.
Bonus Round 10 (In case you think this is too easy): Edo Madara (not 10 tails)
Big trouble for Katakuri and Madara has no reason to fear him. He is immortal and Katakuri can´t put a Edo Tensei down without sealing or erasing abilities. Madara at the End can make Katakuri sleed with his Mokuton abilities. Going with Madara here.