You must do 1003 pushups in one go. This can be done by holding the Up on the D-pad.
This can be tiresome after a few minutes so, using the Xbox Accessories app, I altered the Controller Button Mapping to switch the "Up" on the D-pad for the "X" button. That way you can hold the button of your preference, for as long as it's needed, it takes some time after all.
Any button except for the triggers, the app won't allow those. This makes it more bearable and you won't let go of the button by mistake, only to start all over again. Cheers!