The towers and spines of the Traverse between Atlantic Peak and Fletcher Peak look pretty daunting from both Mayflower and Mc Cullough Gulch.
They are still pretty daunting when you start climbing them but with proper route selection one can stay on (or at least close) to the ridge line most the time and keep it to Class 3 - 4.
I highly recommend to do the Traverse from Atlantic Peak to Fletcher Peak and not the other way around.
Gain the summit of Atlantic Peak from either Mayflower or Mc Collough Gulch and scramble along the ridge southwards in the direction of Fletcher Peak. You will have to climb over 5 major towers and a couple more smaller spines.
Only experienced climbers should undertake this route. The ridge is pretty complex, and each tower could be tackled in various ways - I am sure you all will have fun figuring it out without any further details. Should you get stuck, just keep on looking, there will be Class 3 - 4 option for each of your route problem.
Close to the center you will hit a vertical portion, this is the only place where you cannot stay at all close to the rige line without technical gear - this one can be easily passed on the Eastern Side.
The biggest challenge is the last major tower before Fletcher Peak. The cliff to the right of the tower's highest point is offering several routes up to the top. Cliff is about 60 ft high and it is easy to climb into a deadend - so plan your route carefully. A slip and fall would be most likely fatal.
If you climb to the far right of the cliff you could avoid this challenge pretty easily by reaching the block fields on the back of the tower - but what fun would that be.
Essential Gear/Mountain Condition
Bring your helmet and leave your vertigo at home.
Lots of lose rock.
Climb only at dry conditions.
Rain or snow could turn this climb into a very dangerous undertaking.
Be off the ridge at noon to avoid thunderstorms