Just want to thanks for the contribution in this community, would like to share the itinerary I found. Which is about 3000 Euro or 3500 USD, if you have existing mile with M&M or M&S, it will bring you cheaper to 2500 Euro or less than 3000 USD
for September and October

anywhere from Europe - IST (book as return ticket with last leg)

Tuesday IST HRG 7:45-10:30
Tuesday HRG MEL 11:25-19:25
Wednesday MEL-SAO 21:20-3:00+2
Friday SAO-IST 04:10-22:55 (book with award ticket with M&M or M&S, it will lower your cost to 500 euro or less with existing miles, for M&M, use payback point transfer & subscription of magazine to acquire mile)

Friday IST-KWI 02:00-5:40
Saturday KWI-EWR 06:35-22:35
Sunday EWR-IST 00:30-17:15 (book as KWI-EWR return as it is almost the same as one way ticket, skip the last leg of IST-KWI)
Sunday IST- your Europe home.

this is a 6 days schedule to complete the challenge. However, if time allows, I would suggest to stay in each place, grab an açaí bowl and wandering around beautiful park in São Paulo, check out beautiful restaurant in New York and Melbourne, have a short beach vacation in Hurghada, instead of just fly and go, it will add more fun with your world travel.

from North America is similar, just do the EWR-kwi route as multiple stop ticket. (EWR-KWI, KWI-IST, IST-EWR as last leg)

In general, M&S has low redeem value nowadays, it is insane to buy miles with $20-30 for 1000 miles, most of time it offers a value of 0.6 cent per mile (0.5 cent euro) for economy flight, business ticket requires often much more extra mile, with low availability. Make it unattractive. You might just buy the ticket directly, and there are other competitors offering similar or lower price nowadays. The only reason I was thinking is the flight to Russia or TK special niche, which mile ticket offers a good value in holiday season, otherwise I don’t really see any incentive of doing this besides from the fun of getting one million miles. Given the time cost is high. However, if you are already planning to fly with TK to Australia, then greeting this award is just a step away, as 3 continents are fairly easy to do. Otherwise the time cost is just too high. Miles & More offers a better redemption nowadays. As M&S mile devalues a lot.

best for all who want to do this challenge