I actually have a Splitting Image I've been heavily investing in now, so I can give some more advice about how here SA1 works.
1) The immunity flips on and off. I guess this would be harder to notice when she's on defense and constantly getting pounded, but any time she has more life than her opponent her immunity immediately goes away, as does the regeneration. Which is good news in terms of not needing to get things right the first time you try to block her immunity.
2) It's hard to get cursed at the right time playing her on offense, but when I have been it does seem to **** with her SA1 royally. If her immunity doesn't proc when it's supposed to, getting it to later is tricky. I'm not entirely certain what causes it to proc and not proc at that point, but it doesn't just come up as soon as curse ends even if I'm then at lower life. I don't believe the immunity procs even if someone else tags in. So having less life than her, cursing her and then taking her down with debuffs does appear to be an option, even if you don't sustain the curse debuff. Could use further testing, but I need to figure out a safe and consistent way to get cursed.
(Now there's a sentence to write down in a journal somewhere.)
Anyway, hope that helps, what with the Fukua prize fight being back!