There are seven unlockable characters in Sparring mode. Each of them is unlocked by defeating a separate boss in STORY mode. To find out what act you can fight the boss in, put the cursor on the character you are interested in and read the description that appears instead of their avatar above.
The character will be unlocked if you’ve beaten the right boss in STORY mode on any one of the save slots on your Nintendo Switch profile (see “How does saving work?”).