I picture something much more industrial than we usually see from the Federation - basically a factory in space. It's overall configuration would be a long box. The ship would be as wide as it could be while still reasonably being able to generate a slipstream corridor, and it would be about 4/5ths as tall. It would then be rather long to compensate for it its necessary volume, perhaps 6 times as long as it is tall. The port and starboard sides would be rounded into arcs, as if it was designed to just barely fit in the corridor (kind of like a Puddle Jumper in Stargate Atlantis). The warp nacelles would be on the top and bottom of the ship, hugging relatively close so as to fit within the circumference of the circle that would be formed by the sides of the ship if the arcs were to be extended to a full 360 degrees. The top and bottom hulls of Achilles contain large, square doors that would open to reveal empty space where the industrial replicators could create large parts for the ships, such as hull plating or even nacelles (when I originally pictured it I thought they might be large enough for a single ship to squeeze in, like a moving space dock, but Mage's comment upthread regarding it not being big enough to fit a ship inside it debunks that). One of these ports could also house the fighters.
Overall what appears in my head would fit visually more with the Stargate universe than the Star Trek universe, but then again Achilles isn't exactly a traditional Federation vessel - I figure a more industrial look, prettied up in Federation colors, is perfectly plausible (though I'm sure there is some description of Achilles that contradicts everything I've imagined, beyond even the aforementioned dimensions).