Hutshepsut is defined as “Spiritual” and “Creative”
“Spiritual” means you have “No anarchy” during revolution. Thus you should change your civics and/or religion frequently (there is a general limit of 1 revolution in 5 turns however). Of course, when doing so you must take into account the effects of the chosen Civics and Religion. Temples are constructed at double speed, meaning that you should discover Priesthood and maybe think of founding several religions. Building missioners is advisable in order to spread religions across your cities, as it will lead to more happy people when switching to “free religion” civic in modern times.
Being “Creative” means you have +2 culture in each city per turn. This will lead to your territory (defined by “Cultural borders”) growing rapidly and can save you building obelisks in your cities. With several wonders built you might even consider a cultural victory (though it is very hard to achieve). Theatres are built at double speed, giving you even more culture, and Coliseums (also double speed) will make people happier in your growing empire. Discover construction (a valuable technology in any case) as soon as possible, and acquire Drama when you can. The Globe Theater is very achievable as well.