The Achille is NOT a typical lever machine, nor should you treat it as such. It's a lever-driven heat exchange espresso machine. Techniques that work for spring levers (e.g. Elektra MCaL) or direct piston levers (e.g. La Pavoni EP) will not immediately translate.
If you have experience with a HX, the cooling flush will make sense right off the bat. I think you'd be better served if you think of the Achille's lever as a replacement for a vibe pump.
I had hands on a friend's Achille for about 2 months, and couldn't come close to either my Cremina or Coffex, but that may be due to some leaks and needed maintenance. For me, the closest thing to success was going to extremes; grind fine and dose low (14g), or grind coarse and go high (17.5g). Any middling doses got washed out, regardless of temperature.