The path for the Labyrinth of Thalassa is straightforward. The only thing to note is when you pick up the "Faster" token, wait until you have 01 second left on your action cooldown before attacking Siren. This will allow you to utilize the bonus for the remainder of the battles. (Note: it only reduces the waiting cooldown by half for movements, attack cooldown is still 30 seconds.) Doing this will allow you to consistently finish around 3:11 to 3:20 for full transcendence and drachamas.
Actually, the Faster does not affect the attack CD, so you should apply it after attacking Siren, just before the Attack CD expires.
Also, might as well hit Polygonos from the side; same amount of spaces and ya might be able to refrain from replenishing if you're a little light on the cloaks and armor