how the heck am i supposed to do this

ok so i’m pretty new to rdr1 and im at the mission with west where you have to rush him to armadillo. HOW THE HECK AM I SUPPOSED TO DO THAT. the first few times i was just having trouble driving and shooting at the same time AND THEN AFTER I MANAGED TO SHOOT THEM ALL, OF ALL OF A SUDDEN HIS HEALTH STARTED DROPPING SUPER FAST WHEN IT WASNT PRIOR? how the heck am i supposed to do this mission. plz help. i dont need someone telling me its a skill issue.. yeah i know im new to this series