requestDGAE.js

var request = require('request');
var fs = require('fs');

var headers = {
    'Origin': 'https://www.siass.unam.mx',
    'Accept-Encoding': 'gzip, deflate, br',
    'Accept-Language': 'es-ES,es;q=0.8,en;q=0.6',
    'User-Agent': 'Mozilla/5.0 (Macintosh; Intel Mac OS X 10_12_1) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/54.0.2840.98 Safari/537.36',
    'Content-Type': 'application/x-www-form-urlencoded; charset=UTF-8',
    'Accept': 'application/json, text/javascript, */*; q=0.01',
    'Referer': 'https://www.siass.unam.mx/',
    'X-Requested-With': 'XMLHttpRequest',
    'Connection': 'keep-alive'
};

var dataString = 'sistema_pertenece=dgae';

var options = {
    url: 'https://www.siass.unam.mx/escuelafacultad-ajaxlist',
    method: 'POST',
    headers: headers,
    body: dataString
};


function firstCallback(error, response, body) {
    if (!error && response.statusCode == 200) {
        var inst = JSON.parse(body);
        for (var i = 0; i < inst.length; i++) {
          var optionsEscuela = {
              url: 'https://www.siass.unam.mx/carrerabyfac-ajaxlist',
              method: 'POST',
              headers: headers,
              body: "escuela_facultad_id=" + inst[i].id
          };
          request(optionsEscuela, callback.bind({
            id: inst[i].id,
            name: inst[i].nombre,
            length: inst.length
          }));
        }
    }
}

function Carrera(id, name, carreras) {
    this.name = name;
    this.id = id;
    this.carreras = carreras;
}

var json = [];

function callback(error, response, body){
  if (!error && response.statusCode == 200) {
      var carreras = JSON.parse(body);
      carreras.map(function(obj){
        delete obj.created_at;
        delete obj.updated_at;
        delete obj.nivel;
        return obj;
      });
      var inst = new Carrera(this.id, this.name, carreras);
      json.push(inst);
      if(json.length == this.length -1){
        console.log("Saving");
        write(JSON.stringify(json));
      }
  }
}

function write(json){
  fs.writeFile("unam.json", json, function(err) {
      if(err) {
          return console.log(err);
      }
      console.log("The file was saved!");
  });
}

request(options, firstCallback);