Wow,that was a long writeup,how long did it take you to do this?.
Tsunade can definately beat her share of akatsuki members,but the others are just a bad matchup,
she would definately have beaten most of the paths if she was at full power when naruto showed up,but deva and his CT would be too strong,nagato as well would be too much even for tsunade and jiraya,his rinnegan techs are haxed,but if nagato dosent use gedo or CT,tsunade would push mid diff with katsuya because of her abilities. She would beat animal,naraka,asura,preta and human,but deva would be too much,so she looses to pain high diff,that's nothing to be ashamed abt.
Tsunade would wreck kisame as she uses taijutsu which is kisame's weakness as he wont be able to absorb anything,she can jump high in the air easily,we saw guy go through water dragon,so tsunade can as well,her immortality tech will allow her to witstand being drowned for an extended period of time,not to mention she can just summon katsuya inside there toewcape the dome.
Tsunade would beat hidan,as she can easily blow his upper body apart and bury him.
Tsunade would beat zetsu easily,no need to comment.
Sasori isnt much of a problem,yon seal release heals all poisons,and tsunade can use her strength to smash his puppets,and use katsua to split and 'absorb' the puppets like katsuya did against the villagers of konoha to save then from CST,while she handles the real one. Sp tsunade wins that one.
Kakuzu looses as well,she tanks all his attacks and punches his stomach clean off,i doubt a new heart can fix that,doton:domu isnt anywhere near as strong as madara's susanoo,which she broke through like glass,all his attacks will knock her back at most.
She would beat konan as well,as she has far more chakra than konan and would outlast her,and katsuya would melt konan's paper easily,
deidara would be tricky,as he is long ranged,however tsunade seems to be raiton as she used it on kabuto,and it definately showed signs of lightening release,she could easily tank c1 and c2,katsuya could absorb and protect her from c3 as her mini clones protected many people from CST,however,if tsunade is infact raiton,then she could use the attack she used on kabuto,on the c3 clay structure before it hits,however unless she sees what c4 does(killing birds and disintegrating them for instance like what happened to the bird in the fight against sasuke),she would fall for that,also c4 dosent have a very long range,with intel however c4 isnt a problem as she can easily dodge it or go past it's area of effect,deidara also dosent have unlimited clay,so she could potentially outlast him,she can jump insane distances,as she jumped above manda and drove bunta's sword into his mouth without anyone even noticing. So without knowledge,deidara would take it high diff more times,but with knowledge,temari wins.
Itachi would be really tough,however if itachi stays 3t,he looses. What you said abt katsuya melting tsunade's skin to escape ama as quite smart.tsunade can also rip out her own skin,also ama burns slowly and tsunade wears clothesxd,so if she is hit on the body,she could take off her clothes

,also sick itachi can't hold susanoo for 5 minutes,tsunade can just hide it out and stall until itachi looses stamina,totsuka is snapped in half,katsuya could use her acid mist to distract itachi,who bu the way can't use ama while in susanoo as he would most likely die,so tsunade can give katsuya the getgo to attack itach's susanoo from the from while tsunade smashes the back,katsuya can divide to escape susanoo arms or blades and then reform again to attack. Tsunade fought 5 ems susanoos without getting caught,i am sure she can take one ms susanoo. However,this fight would be high diff for itachi most of the time,but depending on events,tsunade would win.
Tobi beats tsunade and basically anyone bar edo madara for obvious reasons,however,if km naruto pushed a hachibi tbb woth one hand,v1 raikage as said by naruto would kill him with 1 punch,v2 raikage couldnt scratch ribcage susanoo by himself(madara),tsunade smashed complete susanoo and madara to pieces with a punch,she can definately deflecta tbb from any of those bijuus,but not simultaneously.
So thatz's abt 6-7 akatsuki members she beats. That's quite good for the 3rd strongest kage.