I Have the "Shotgun" Delthea

She could be one of those heroes who could benefit from the Sweep skills. I don't have her, so I can't really tell for sure.

I honestly think giving her Death Blow is a bit too much considering her somewhat average SPD which is the more important stat to improve. For her A-slot skill, Darting Blow may be better given her stat spread and this'll help her more than Death Blow. Given that, Desperation paired with Darting Blow will make her an excellent nuker while leaving her with some form of defense against Mages considering her decent RES.

For B, I always consider vantage :3 it's just so good

I'd recommend ronanxthalia's advice, with one important addition: Ardent Sacrifice. With Desperation 3, using that skill once automatically puts her in Desperation range and gives her a de facto brave tome. It takes an extra turn to set it up (one of your teammates has to get injured first for her to use AS), but that time is worth it in terms of her dying vs not.
This is the same recommended build for Linde (who has AS prebuilt), Nino, and Tharja, very similar types of glass cannon mages to Delthea.

For a budget version, Death Blow works just fine. It really acts as a 'shotgun', you can reach 63 attack with just hone att on initiation.

For a B-skill, Vantage is good IMO. A bow user initiating on Delthea will often mean a OHKO, whereas if Delthea gets the first attack, that could be the other way around.

But, LnD+Desperation is the best combo. If you have the means, that set-up won't disappoint.

So as someone who runs Delthea, I wouldn't suggest taking Death Blow off of her. Here is the thing: she can't take a counter-attack from any physical unit period.

You basically have two good options with her IMO:

1) Death Blow + Blue or Red Tome Breaker - Some say Lancebreaker, but again, if you're taking a counter-blow from Camus (the only lance user you're likely to run into with a distant counter ability). she's dead anyway. Distant Counter Effie is going to kill her with or without Lancebreaker. Her high Res lets her eat a blow from any mage that isn't green save Cavalry-buffed Reinhardt initiating with 2 attacks (can't do much about that one). Blue Tomebreaker lets her secure kills on Linde, Olwen, etc, and she trashes Reinhardt on initiation. Red Tomebreaker is generally overkill except I believe in the case of Katarina. I've seen some suggest Swordbreaker because of extreme cases of Ryoma surviving a blow from her, but it's too niche IMO.

2) Death Blow + Desperation 3 + Ardent Sacrifice - Ardent Sacrifice is generally the only safe way to get her into Desperation land. Use a tank of some kind to eat some damage, then put her in Desperation mode. The downside of this build is she won't be able to attack anything until the third or fourth round of combat.

Don't take any of this as a knock on Delthea btw. I think she's the second best blue mage in the game atm with her insane buffs. So far, I haven't really had much trouble dispatching Ryoma/Xander in a single blow thanks to the fact her attack power reaches 60+ with DB and buffs. For what it's worth, I actually went with Blue Tomebreaker against the advice of all the Desperation builds out there as there are only so many copies of Desperation 3 to go around, and I find it just fine.