What to do with -spd,+atk normal Azura?

Tl;dr: Slaying Lance+ (+Atk or +Spd) weapon; Moonbow special; Death/Darting Blow A passive; Guard, Hit and Run/Drag Back, or Wings of Mercy B passive; and a defensive or flat stat-increasing seal. Everything else is fine.

-Spd +Atk is still really nice (and I assume you're talking about the default Azura, or Lance!Azura as I like to call her). While 34 Atk isn't amazing it's still pretty high and nothing to scoff at, and while she can't double too many targets without skill or ally assistance with 30 Spd she's still able to prevent a lot of foes from doubling her without skill/ally assistance themselves. Having Speed +3 as her default A skill bumps this up to 33 Spd, placing it as equal to a Spd-neutral Azura without it.
The fact she has 34 Atk means Sapphire Lance+ places her at 46 Atk (though that weapon is mostly trash anyhow). If you chose to replace that with a Slaying Lance+ with its 14 Might, that puts her up to 48 Atk. Choosing to upgrade it further with its +Atk upgrade gives it an additional 2 Might, placing Azura at 50 Atk; choosing the +Spd upgrade puts her at 36 Spd which makes it hard for anything to double her unassisted, at the cost of putting her back at 48 Atk. Give her Moonbow, with its reduced charge time of 1, and she'll be able to dish out quite a bit of damage when she's not Singing (regardless of which Slaying Lance+ upgrade you choose).
To be honest, I wouldn't even bother with sticking with Speed +3. Though it is pretty high, it's definitely not reliable enough for any sort of Desperation build. Darting Blow 3 is a nice alternative, but perhaps Death Blow 3 would be better if you wanted to focus more on Moonbow-spamming offense. If you REALLY want both Atk and Spd, you can sacrifice a rare unit for Swift Sparrow 2, or even sacrifice a Nephenee for Atk/Spd +2 (though I wouldn't waste that on her, considering she herself has Slaying Lance+ AND Wrath 3 as other better-given skills). Guard 3, or perhaps one of the unit-moving skills like Hit and Run or Drag Back, would be fine as B skills (just because you build offensively doesn't mean she's a purely offensive unit)...and I wouldn't bother much with a Breaker skill since her defensive stats are pretty bad. Her optimal choice, though, would be Wings of Mercy 3 due to her status as a Sing/Dance unit. Her default Fortify Res 3 is fine as a C skill, though Spur or Drive skills are always better on teams that don't include Blade Tomes.
Finally, her choice of seal...I'd probably stick with the defensive options like Fortify Def or Hone Atk or Spd (useful alongside her default skill), or Drive Def. If you want to have her more offensive you could go with Attack +3 alongside Death Blow, or even perhaps Speed +3 if you want to stick with her default duplicate so she can have more speed (also works with Darting Blow A). ABSOLUTELY DO NOT go with Heavy Blade, because as good as 50 Atk is it's NOT reliably higher than anything except a staff user...it'd just be a waste.

She's a Refresher. They're never going to be worthless.

She's a Dancer... at the very most, you need them to only cover whatever color they're strong against, and that's what TA/Gem Weapons are for.

Your best option is Slaying Lance +(+spd), Moonbow, TA, WoM, C slot and seal are flexible. Can be Hones, Ploys, Drives, or even speed +3.

Your "budget" option is to keep that Sapphire Lance and switch out TA for Fury, then the rest of what I said above.

She'll still perform, don't worry. My PA! Azura is actually +atk/-spd and she carries the AA matches she's in (granted, PA! Azura has Uror but still).