How to parse large amount of JSON data on mobile browsers?

I have this use-case where I work on a mobile app, that runs inside a browser or (if android) inside of a WebView. This app needs to work offline, so I need to download big amounts of data (25MB-100MB) at once, parse it, and save it in the local database (indexeddb or websql).

Especially on mobile, parsing huge amounts of data is very slow, and can potentially break the app. The amount of memory used is not enough and the app can crash.

What would be a good strategy/solution to fix this issue?