|Olivia is one of the few currently available dancers in the game, and the only one who is red. Her defensive stats are respectable, and her speed is in a good spot to avoid a lot of frequent doubles. This comes with the shortcoming of her low Atk stat, but with a few changes to her kit, she can still manage to hold her own in fights.
To start off, let’s consider Olivia’s choice for special. Olivia being a dancer shouldn’t need to be in the thick of combat very often. You want to keep her encounters short and potentially position her away from any retaliation/enemy initiates on Olivia. For this reason it’s optimal to run a low CD special because it’s more likely that it’ll actually put in some work as opposed to long high-damage specials. This is why we have either Moonbow.
Moonbow helps her kill certain units she had trouble killing prior. These units include Sophia, Seliph, Chrom, Alfonse, and Merric. The relevance of these matchups is up to the player. These aren’t very commonly seen units, but are still worth accounting for additional coverage.
Now to consider her weapon with respect to the rest of the build. Ruby Sword+ is a solid go-to option that allows her to more definitively handle green units at the expense of doing poorly with blue blue units (who she shouldn't be facing anyway). It allows her to tank popular green units such as Hector and also leaves her at higher levels of HP to deal with any additional green units she may need to face off.
Wo Dao+ can also be considered as a weapon option. Although she no longer has the increased weapon advantage against green units, the flat +10 damage upon special activation remedies this loss. Paired with the 2-charge special Moonbow, this allows Olivia to dish out formidable damage. For example, she defeats most Red Swords with Wo Dao+ if she can get the double. Additionally, without the increased weapon disadvantage against blue units, on a defense team, this makes it difficult for enemy blue units to bait Olivia.
Silver Sword+ is a solid budget option which provides Olivia extra Atk over Ruby Sword+, and also comes in Olivia’s base kit. Silver Sword wins a few more matchups over Ruby+, like Ike, Eldigan, and even a few blue units like Peri, Florina, and Clair (but she should avoid matching up against blues regardless). It kills all the same greens as Ruby+ with the exception of Anna, who ends up killing Olivia. The downside to this is that she kills greens in a less clean manner, so her HP will be lower after each combat when using Silver+ vs Greens as opposed to Ruby+. This is due to the free TA that Ruby+ provides which allows Olivia to turn ORKO’s (one round KO’s) into OHKO’s (one hit KO’s).
Note that Silver Sword+ on top of TA is not comparable to Ruby Sword+ build. This is because of Fury, which not only gives her the additional 3 Mt she's missing with Ruby Sword+ vs. Silver Sword, but also gives here +3 in Spd, Def, and Res as well. Not just 15 Mt and the TA effect that Silver Sword+ and TA give. Also, if a + weapon is too expensive, Ruby Sword (no +) is also fine if your plan is to primary kill greens. She still kills greens very potently, but due to the lower Mt, loses the ability to kill certain reds like Chrom and Alfonse.
For her A skill, Fury 3 is a very solid skill for most units, and Olivia is not an exception. Dancers have very low base stat totals and Fury 3 helps them gain a bit of leverage and beefiness to their defenses. The extra Spd, Def, and Res makes her a lot harder to kill. The chip damage is negligible because she will be dancing most of the time and won’t be in combat too often. Life and Death 3 is NOT a viable alternative because the extra Atk and Spd at the expense of Olivia's Def and Res is not optimal. You want Olivia to be survivable by accounting for some worst case scenarios where she needs to take a hit or suffer some retaliation before killing a specific unit.
Wings of Mercy 3 is the recommended option as it gives Olivia more global presence and mobility. Swordbreaker 3 is a tech option because the ability to double any red sword in the game is very strong and allows her to check both greens and reds. Popular units like Lucina/Ryoma with their most common builds get slaughtered by Swordbreaker 3. It’s also insurance for if they ever initiate on your Olivia and for other Red Swords who may be running Swordbreaker 3 themselves.
Her C skill is flexible, but she comes with Hone Atk 3 which is a strong option. A player's team might need another Hone though, so any other Hone that a team needs can also work. Using a Threaten is NOT recommended though, because Olivia will rarely be in a frontline position to utilize a Threaten passive.
Finally, for her IVs, +Atk and +Spd are viable options as they increase Olivia's offensive power. The former allows her to hit a little harder while the latter allows Olivia to increase the number of units she can double (especially important in a Wo Dao+ build). -Res is a recommended bane unless a player is using Olivia as green mage bait (in a Ruby Sword+ build), in which case -Def can be an option as well.