At the beginning, leap over the leaves (you can do this) on the right side of the block that you start out behind. Agreus is on his way over, so at that point you'll want to switch to your throwing daggers as there are two bells you can ring to draw his attention to. One of them is very close to you, and the other one is to the left of the beginning point further away. After you've crossed the leaves to the right, throw a dagger at the one further away, and then immediately start moving toward your goal.
At this point you can get a little further in, but STOP as soon as Agreus reaches the bell you shot, and throw another dagger at the bell near the point where you began. This will distract him yet again, and you can start moving again. The idea is to use your MIST FORM to move over large stretches of leaves, and ALSO to disappear before Agreus sees you. He is pretty tough to avoid, so just use the environment and your mist form to plan ahead.
If you manage to make it to the button that opens the gate, good news-- as long as you activate it, even if you fail, the gate will be forever open, so even if you're caught before you can get to the gate, your next run is simply getting to the gate. Once you're through, it's over. Finally, if you get close enough to the gate button, well in my case I simply made a mad dash for the button and hit it as Agreus was coming for me.
It's honestly not that hard, especially if you make use of those bells at the beginning.
To summarize:
-move over the leaves to the right, throw dagger at bell furthest away
-make some progress as Agreus investigates
-stop whenever you're about to lose sight of the bell closest to the starting point
-fire another dagger at that bell
-keep moving forward
-use mist form to glide over leaves undetected
-use mist form to disappear before Agreus sees you
-keep in mind that your mist form is very temporary so use it tactfully
-when you get close to the button that opens the gate, just make a mad dash for it if possible
-once you get the gate open, it's open for good even if you fail