For some unknown reason the stage 5 of the challenge mode (INCREASE MAX HP) for the US and EU vers. of this game DON'T WORK properly, aka GLITCH on Japanese PS4 consoles.
The game don't allow in any kind of form the purchase option for MAX HEALTH HP, making impossible to finish the stage. The wall shop option that should have 3 pages only have 2, the middle page that should have MAX HEALTH HP to purchase don't exist and the third page replace the second and have the strange name FITOS VO.2.
If you are in the same situation and want proceed, you need quit this stage and start from stage 6. The completion challenge trophies are not mandatory for consecutive cleared stages, can be any random order from those 30 stages available to play.
The Asia ver. don't have any similar issue regarding this challenge mode stage 5 glitch on the Japanese PS4.