You need to back up a couple steps and, in consultation with your client, work out a threat model. (Yes, that's a link to a 600-page book; yes, I am seriously recommending you read the entire thing.)
A threat model starts by asking questions like
- Why does the app need to store this sensitive data in the first place?
- Can you avoid storing it at all?
- Can it be thrown away after a short time?
- Does it truly need to be accessible to more than one device?
- If it must be accessible on more than one device, does it need to be stored on more than one device?
- Who are the people who are allowed to see each user's sensitive data?
- Can this list be made shorter?
- Who are the people who may come in contact with each user's sensitive data while trying to do their jobs, but have no need to know it?
- Can this list be made shorter?
- Can the data be rendered inaccessible to them without harming their ability to do their jobs?
- If it can't be inaccessible, can it at least be made incomprehensible? (This is what encryption does, in the abstract: it renders data incomprehensible.)
- Who are the people who want to see the sensitive data, but are not allowed?
- What opportunities do they have to get at the data?
- What do they want to do with the data once they have it?
- How angry will they be if they don't get what they want?
- How much money, time, CPU cycles, and human effort are they willing to spend?
- Do they care if anyone knows they have seen the data?
- Do they want to access specific users' sensitive data, or will anyone's do?
- What do they already know?
- What do they already have access to?
Once you know the answers to these questions you will be in a much better place to figure out what to do.
Keep in mind that there might be more than one answer to each set of questions, especially the ones dealing with the attackers (the people who want the sensitive data but are not allowed to have it). If you can't think of at least half a dozen different archetypal attackers, with different motivations, goals, and resources, you've probably missed something.
Also keep in mind that the attackers who cause you (and/or the client) the most trouble, are the most likely to make a giant splash in the media if their attack succeeds, or who do the largest amount of aggregate damage, probably are not the attackers who can cause the greatest harm to individual users if their attack succeeds. Your client's company rationally cares more about aggregate damage, but the users rationally care more about harm to themselves.