Disclaimer
This list of completion times is based on ones that earned me gold medals in each of the challenges, and therefore does not likely represent the exact times needed to earn gold. Since the developers seem to keep the medal times neat (i.e. 3:40:00 instead of 3:38:45) I will post my approximate times in a similar standard. Most of my scores are pretty modest and probably resemble the bare minimum for gold, but anyone who can contribute more accurate gold times will be duely credited in the body of this guide.

Challenge Name Minutes:Seconds

MM1 REMIX 1 1:55

MM2 REMIX 1 2:30

YELLOW DEVIL 1:30

MECHA DRAGON 0:25

CRAIG'S CHALLENGE 2:45

MM1 REMIX 2 3:40

MM2 REMIX 2 4:00

MM1 ROBOT RUSH 1:40

WILY MACHINE #1 0:45

MM1 MEGAMIX 4:00

MM2 ROBOT RUSH 2:05

MM2 MEGAMIX 4:45

WILY MACHINE #2 0:30

MM1-2 MASHUP 5:30

MM3 REMIX 1 2:26

MM4 REMIX 1 2:10

YELLOW DEVIL MK-II 0:46

SQUARE MACHINE 1:00

MM3 REMIX 2 3:00

MM4 REMIX 2 4:36

MM3 ROBOT RUSH 2:45

WILY MACHINE #3 0:40

COSSACK CATCHER 0:35

MM3 MEGAMIX 4:00

MM1-3 MASHUP 5:45

MM4 ROBOT RUSH 4:30

MM4 MEGAMIX 5:30

MM1-4 MASHUP 6:40

WILY MACHINE #4 0:50

MM5 REMIX 1 2:45

MM6 REMIX 1 2:30

BIG PETS 0:27

MECHAZAURUS 0:35

MM5 REMIX 2 6:00

MM6 REMIX 2 5:15

MM5 ROBOT RUSH 3:50

MM5 MEGAMIX 5:45

WILY MACHINE #5 3:15

MM1-5 MASHUP 6:50

MM6 ROBOT RUSH 3:45

MM6 MEGAMIX 4:55

WILY MACHINE #6 0:50

MM1-6 MASHUP 6:50

ALL APPEARING BLOCKS 2:20

DR. WILY FOREVER 8:15

ALL ROBOT RUSH 20:00

MM1 ROBOT RUSH (NO ITEMS) 3:19

MM2 ROBOT RUSH (NO ITEMS) 6:50

MM3 ROBOT RUSH (NO ITEMS) 7:30

MM4 ROBOT RUSH (NO ITEMS) 7:20

MM5 ROBOT RUSH (NO ITEMS) 6:45

MM6 ROBOT RUSH (NO ITEMS) 6:30

ALL APPEARING BLOCKS (NO ITEMS) 3:20

ALL ROBOT RUSH (NO ITEMS) 40:00

Big thanks to Black_Clone, TricksterTravvy, Dr. Cheis, ©HiHoFai™, Catalyst, tiago.trigger, dart193, Alnemesis, Galewin, 3SemiN8, Director Bison, Reik Val, Chauckles, cbp105, kirbyte, Underkill, HauntedToast, Raven, Remoba, Legend Ice, v0idpwn, Desticler, Kavaliro, Mephisto, Dustinaux, and A Competitive Bombsquad Player for helping to improve this guide.