As long as Archelos is tapped, other permanents enter tapped.
As long as Archelos is untapped, other permanents enter untapped.
"Life ... is not ... a race."
(10/11/2020)
If another replacement effect says that a permanent enters the battlefield tapped while Archelos is untapped, the entering permanent's controller chooses whether the permanent enters tapped or untapped. If a permanent is simply put onto the battlefield tapped without a replacement effect being applied, it always enters untapped if Archelos is untapped.
(10/11/2020)
If more than one Archelos is on the battlefield, the controller of an entering permanent chooses how to order the replacement effects.
(10/11/2020)
Archelos's abilities don't apply to itself as it enters the battlefield, nor do they apply to any permanents entering the battlefield at the same time.
