And I don't think I can see her as a Palutena echo.
Let's see what she'd need:
Her tilts all use a staff. Azura would use a spear
For some moves, Palutena uses a shield. Azura can't really replicate that since she does not use a shield. However, the shield is only used in Back Air and Dash Attack and thus can be replaced
For Smashes, she'd need wings. Azura does have dragon blood, so she could feasibly pull it off, albeit with water wings like Steven Universe's Lapis. Alternatively, she does have a Pegasus in some classes. Summoning the wings from that could prove to be a valid explanation.
The Column of Light Up Smash is now a Geyser from the Dragon's Vein ability
Up Air uses some sort of angelic energy. Some water effects would make this move feasible for Azura to perform (hah) too
Now for Specials:
Auto-Recticle could be water droplets summoned from her pendant.
Explosive Flame can be a bubble that pops
I don't know what Palutena's current up special is. Azura covers herself in quite a lot of water in her dancing cutscenes. Possibly enough to simulate a warp.
Down Special is Counter-Reflect. Azura summons a water wall in one of the cutscenes and summons waves for most attacks in her Warriors moveset and the counter is done with the staff/spear.