Firstly, welcome to FT !

The Alliance wide upgrade program is not yet rolled out amongst all the carriers. The current participants are NZ NH OZ OS LO LH LX SQ SK TP TG and UA. (I think UA has pulled out of it recently).
However, like the FF reward schemes, each carrier has it's own rules/policies in place as to how they participate in the scheme.
AFAIK, SQ only has the interline upgrade reward agreement with NH OS LO LH LX and TG. From memory, only tickets in classes Y M B S or E are eligible for the upgrade - and I believe it's a lot of points to claim them too !!

Your question is probably better asked (and more quickly answered) in the Kris Flyer forum, as it relates directly to the SQ scheme/rules rather than the Star Alliance.

Cheers and Regards.