I agree it is probably a bit ambitious. But a quick suggestion is doable on a paid ticket - I have minimised South America stops, and the ATH-ZRH sector should be surfaced. I have not checked that *A atually operates all segments (DEL-DXB in particluar could be an issue).
This comes to 13 segments and just over 32,000 miles:
del-dxb-cai-ist-ath-zrh-lhr-lis-gru-sfo-akl-syd-sin-del.
this leaves room for additional 3 segments (to cover for inoperable city pairs and may an added city).