She has displayed a very high amount of spiritual power, capable of forming it into the shape of a cat. She is also deceptively strong, able to pick up Kenpachi and leap around Seireitei with his unconscious body. She may look tiny and weak, but she has already shown that she isn't.
Yachiru is really a complimentary character to Kenpachi. That is why we know very little about her abilities in combat. However like Godisme said her spiritual pressure is quite high. Only three characters have ever made the "face" when exerting their spiritual pressure. The first two, Ichigo and Kenpachi, have two of the highest spiritual pressures in all of Bleach. While there is no more evidence to support it, I wouldn't be surprised if Yachiru's spiritual pressure is on the same level as a captain.
Godisme wrote: She has displayed a very high amount of spiritual power, capable of forming it into the shape of a cat. She is also deceptively strong, able to pick up Kenpachi and leap around Seireitei with his unconscious body. She may look tiny and weak, but she has already shown that she isn't.
This and also because unlike some of the other Lieutenants, she can actually breath and function normally around Kenpachi when he's fighting, meanwhile seated officers (like Hinataro) tend to suffocate in his presence. This could either mean she's become immune somehow to Kenpachi's spiritual pressure (which I'm sure is not possible unless you can match the power with your own, e.g., you're just as strong) or she really is powerful.
And if there's one thing Tite Kubo has emphasized in Bleach it is don't underestimate somebody just because of their Age and Height. One example is Wonderwiess vs Head Captain Yamamoto. Kid was powerful :/
Never mind asking why Yachiru is a lieutenant, you have to ask why Omaeda is one...