index.js

import Ember from 'ember';
import AuthenticatedRouteMixin from 'simple-auth/mixins/authenticated-route-mixin';

export default Ember.Route.extend(AuthenticatedRouteMixin, {
  model: function() {
    var app = this.modelFor('apps/show');
    var adapter = this.container.lookup('adapter:application');
    var url = adapter.buildURL('app', app.get('id')) + '/metrics';
    adapter.ajax(url, 'GET').then(function(response) {
      debugger
    });
  }
});

If you plan to stick with this approach, you'll want to change

"adapter:application" to "adapter:app" (if app is the name of the model)

Having said that, I think it's more idiomatic to do the following:

// app/models/app.js

export DS.Model.extend({
  metrics: DS.belongsTo('metric', { async: true }),
})

// app/routes/apps/show/index.js

export default Ember.Route.extend({
  model() {
    const app = this.modelFor('apps/show');

    return app.get('metrics');
  }
})