how to manage multiple checkboxes in ember?

Okay further to your additional questions, I've basically finished your app for you:

http://jsbin.com/datojebu/11/edit

App = Ember.Application.create();
App.ApplicationAdapter = DS.RESTAdapter.extend({
    host: '/api',
    namespace: 'fr'
});

/* router */
App.Router.map(function() {
  this.resource('animes');
});
App.AnimesRoute = Ember.Route.extend({
  model: function() {
    return this.store.find('anime');
  },
  setupController: function(controller, model) {
    this._super();
    this.store.find('genre').then(function(genres) {
      controller.set('genres', genres);
    });
    controller.set('model', model);
  }
});

/* models */
var model = DS.Model,
    attr = DS.attr,
    hasMany = DS.hasMany;

App.Genre = model.extend({
    animes: hasMany('anime', {async: true}),
    nom: attr('string')
});
App.Anime = model.extend({
    nom: attr('string'),
    parution: attr('number'),
    synopsis: attr('string'),
    likes: attr('number'),
    auteur: attr('string'),

    genres: hasMany('genre', {async: true})
});
/* controllers */
App.AnimesController = Em.ArrayController.extend({
  genres: Em.A([]),
  selectedGenreIds: Em.A([]), // a set of ids
  selectedGenres: function() {
    var genres = this.get('genres'),
        selectedGenreIds = this.get('selectedGenreIds');
    return genres.filter(function(genre) {
      return selectedGenreIds.contains(genre.get('id'));
    });
  }.property('selectedGenreIds.@each', 'genres.@each'),
  selectedAnimes: function() {
    var allAnimes = this.get('model'),
        selectedGenres = this.get('selectedGenres'),
        filteredAnimes;
    // for an anime to be shown, it has to have at
    // least one of its genres selected
    filteredAnimes = allAnimes.filter(function(anime) {
      return anime.get('genres').any(function(animeGenre) {
        return selectedGenres.contains(animeGenre);
      });
    });
    return filteredAnimes;
  }.property('model.@each', 'selectedGenres.@each', 'genres.@each')
});
App.GenreController = Em.ObjectController.extend({
  needs: ['animes'],
  isChecked: function(key, value) {
    if(arguments.length > 1) {
      // setter
      var selectedGenreIds = this.get('controllers.animes.selectedGenreIds'),
          thisId = this.get('id');
      if(!selectedGenreIds.contains(thisId) && value) {
        selectedGenreIds.addObject(thisId);
      } else {
        selectedGenreIds.removeObject(thisId);
      }
    }
    // always return the value for the getter and the setter
      return value;
  }.property('controllers.animes.selectedGenreIds')
});

/* mockjax */
var animes = [
    {
        id: 1,
        nom: 'Blah',
        parution: 2014,
        genres: [1, 3],
        synopsis: 'Lorem ipsum dolor sit amet, consectetur adipisicing elit. Tempore, eveniet, ab pariatur omnis dolor sunt alias atque voluptate neque reiciendis maiores impedit quibusdam perferendis optio ratione expedita adipisci et. Cupiditate!',
        likes: 206,
        auteur: 'Moi :p'
    }
],
genres = [
    {
        id: 1,
        nom: 'action',
        animes: []
    },
    {
        id: 2,
        nom: 'magie',
        animes: [1]
    },
    {
        id: 3,
        nom: 'amour et amitier',
        animes: []
    },
    {
        id: 4,
        nom: 'aventures',
        animes: [1]
    }
];
$.mockjax({
  url: '/api/fr/animes',
  responseTime: 750,
  responseText: {
    'animes': animes
  }
});
$.mockjax({
  url: '/api/fr/genres',
  responseTime: 750,
  responseText: {
    'genres': genres
  }
});