One right order is: Collar, yoke, one arm [cuff first], other arm [cuff first], front left, back, front right.

Are the wrinkles pretty much the same ones you started with, or are they new ones with sharper creases?

If new, sharp creases, you are probably accidentally ironing creases in the wrong place, or folding it over as you go. Concentrate carefully on the placement of the garment, remembering that fabric will remain prone to creasing while it remains hot.

If original wrinkles which have not gone away: You are probably not using enough heat and steam. 100% cotton needs pretty much as hot as the iron will go (>=3 dots), and as much steam as the iron will produce. Consult the manual (!) for how to ensure the iron is producing copious steam. Typically, you need to put enough water in (not too much), have it set to a high enough temperature, set the steam control valve to maximum, wait for it to heat up to hot enough.

My guess is not enough heat and steam.

Beware! An iron this hot will melt many other garments. But a colder iron will not be effective on 100% cotton. Linen needs a lot of heat too. Look on the care label for an iron icon. The number of dots indicates how hot your iron should be - 1 (coolest, garment at risk of melting if iron set higher), 2 or 3 (hot, garment at risk of not de-creasing if iron set lower). Hotter irons are more effective (speed and quality of output) than cooler ones. In my experience garment manufacturers set the care label conservatively and you can get away with a setting one higher most of the time. But always test carefully first.