You can also use the bind function to bind the context to a specific reference. I find generating a self variable to be a bit of a hack and can still cause problems when your callbacks are calling other callbacks. In the case of the presented code, it would look something like:
success: function(user) {
// Do stuff after successful login.
this.nav.push(TabsPage); // HERE I WANT TO REDIRECT TO THE LOGGED IN PAGES OF MY APP
}.bind(this)
I think the current best practice though is the lambda (fat-arrow) notation you were suggesting.