I am using akali, i send two akali deadly weapon in a occupied battlefield dealing 2 damage each because they are empowered, then i activate my empowered akali legend to send back one of them that deal another 2 damage, now the one that returned to base arrive ready because my legend is empowered, can i send her again for additional 2 damage since the showdown has not yet finished?

No — you can't send her back during the Showdown. The pull-back via Rogue Assassin works (the return Move triggers another 2 damage, and Empowered readies her), but a Standard Move can only be performed in your Main Phase during an Open State, not during a Showdown or Combat (Rule 144.1.c). The unit will have to wait in base until the Showdown resolves and you return to your Main Phase.

And even then, the damage question mostly evaporates: when that Combat Showdown ends, Combat Cleanup heals all surviving units (Rule 466.1.a) — so all 6 damage dealt is wiped unless it was lethal. If you re-enter later in your Main Phase, that's a brand-new combat, her "When I move" triggers again for 2, but that damage will also be healed at that combat's end unless it kills a unit.