Only showing the finals to make the video not very long (Proof is showed at the end of the video with the Fall Guys Tracker).

0:00 - Win 1: Thin Ice
4:12 - Win 2: Thin Ice
6:25 - Win 3: Hex-A-Gone
8:51 - Win 4: Jump Showdown
12:08 - Extra: Pre-Win 5: Fruit Chute (Close Call to lose!)
13:35 - Win 5: Thin Ice
17:26 - Proof of having 5 wins in a row
17:51 - Getting the achievement (Thanks to the support team!)

I did not get the Infallible achievement due to a strange reason, so I contacted support, thanks to them for helping me out!