In SS3, he survived getting struck by lighting and became revitalized in the second round during the fight with him. In SS4, he cut Amakusa in half along with that floating girl (cut scene after everyone's fight with Amakusa) while being some distance away since he's out of shot when it happens. Could have been his Gale Slash or something similar to Raijuta's Izuna techniques.
I'll have to retread a bit from my other post. There are two Amakusa's in SS3 and SS4. According to what I've read, Amakusa's soul was split in two after his defeat in SS1, one half good and the other bad. The playable one is the good half while the boss version in SS4 is the evil half (the blue skin makes me think of a blue meanie). The Amakusa in the SS2 cut scenes is the good half since he saves some of the characters from Mizuki's wrath.
The timeline is SS5, SS1, SS3, SS4, SS2, and the 3D games are chronologically the last. I think SS5 Special might be a dream match but Tenka is most definitely one. So, except for SS5 and Tenka, his appearances in the other games are canon.