If there is an image on Twitter it usually has the format "<someshit>.jpg" or "<someshit>.jpg:large". Change the URL to "<someshit>.jpg:orig" to get the largest resolution image the user uploaded.
https://e621.net/post/show/712619/2015-adam_wan-anthro-blue_eyes-breasts-cheetah-fel
1024x1237
https://pbs.twimg.com/media/CM5GYToWwAE7_Je.jpg:orig
1137x1374
Wow!
Updated by Lance Armstrong