When you first get to Garden of the Hesperides, you will need to use a different path than I describe below in order to utilize the bonuses. Or if a troop replenishment is necessary for your to complete the Garden.
The path I have outlined will give you a finishing time of 333-340 with little effort. It is important to note there is a difference between attacking form the front, and from the flank, a flank attack will give you a 10% attack bonus.
The circles marked in green (Hespera, Mesembria, and Hesperis) will all be flank attacks, which will minimize your troop loss.