Darwin: "Giraffes got their long neck from blind evolutionary selection. Lamarck: "No, that's all wrong, they acquired their long neck through effort!"
To get the topmost left room you should jump in the gravity field. When you are down most you should go right most against the wall. You'll be launched up exiting the tunnel. When you're at the highest point move left and re-enter the tunnel. Do this about 4 times until you're able to get the red cube.
For 'quickly' getting the medium badge continuously upgrade your characters and their skills and follow this order: first campaign on normal, first campaign on hard, second campaign first 13 battles on normal, first campaign on extreme, second campaign first 13 battles on hard, and finally complete the second campaign on normal.
 "Super Samurai Sweeper"){kind=icon}
 "- Music in Motion -"){kind=icon}
 "Revenge of Dog"){kind=icon}
 "Soviet Rocket Giraffe Go Go Go!"){kind=icon}
 "Cell Warfare"){kind=icon}
 "Multitask 2"){kind=icon}
 "The Last Stand"){kind=icon}
 "The Splitting"){kind=icon}
 "Gateway II"){kind=icon}
 "Medieval Shorts"){kind=icon}
 "Bit Blast"){kind=icon}
 "Home Sheep Home 2: Lost in London"){kind=icon}
 "The Illusory Wall"){kind=icon}
 "Mighty Party"){kind=icon}
 "Idle Intelligence"){kind=icon}
 "Fillz"){kind=icon}
 "Stacko Level Pack"){kind=icon}
 "Tower Keepers"){kind=icon}