For her kai ni forms, Zuikaku's is basically a hypothetical remodel where she survived the Battle of Leyte Gulf (October 25, 1944) and received aircraft catapults as originally designed. An alternate second remodel depicts her in a hypothetical armored carrier form a la Taihou.
She has the same set up as Shoukaku's. The only real difference is that Kai Ni keeps her color scheme and camouflage from Kai form (a camouflage kimono and brown pleated hakama skirt) and Kai Ni A restores her original white kimono and red skirt. She also has a different stat spread than Shoukaku, favoring AA and Evasion to her Firepower. She also remodels at different levels: Kai Ni at Level 77 and Kai Ni - A at Level 90.
The main visual differences between Zuikaku K2 and non-remodeled Zuikaku are following: 2 tasukis instead of 1, black thighhighs, and improved rudder footwear. Her flight deck also gains an aircraft catapult on the portside. For Kai Ni A, her flight deck is colored black.
Zuikaku K2 has had 2 seasonal alternate outfits: a Christmas outfit (post #3340291) that regularly appears in-game during the month of December, and a long hair outfit (post #3022277 and post #3022286) for the Leyte Gulf-themed events that took place in 2018.
This tag implicates zuikaku_(kancolle) (learn more).