Each agency starts with a 1 star rank. To level up your agency, you need to fill up all three bars for Excitement, Appeal, and Satisfaction.
Excitement is related to choosing most desired options for your customers in the agency (i.e. destination, meal, hotel, etc.). You know which option is correct by cycling through until you see a smile on their faces. After a correct choice, you will see a yellow star add to your yellow Excitement bar.
Appeal is related to spending money to upgrade your agency. Spend enough to fill the green Appeal bar. The only way to earn money is within your agency. Your work at the destinations will not earn any money.
Satisfaction is related to making sure your customers enjoy themselves at the destinations. Each time your completely fill a red heart of a customer, it will be added to your red Satisfaction bar. Their hearts fill up when they are satisfied (do not have an action bubble above their head). Their hearts empty when they want something (have an action bubble above their head). Keep playing the agency part of the game until you fill all seats of a plane for which you can then go and earn satisfaction at the destinations.
Once you get all three bars full, you will increase your star rank by one and the bars will empty. The progression towards five stars is not linear. The bars take more and more playtime to fill up as your star rank increases. See the General Tips at the beginning of the guide to make these achievements easier.