Solution: Get a list users with recently earned badges

Code:

// Get a list of users who visited the community during the specified period
static string APIQueryLastVisitedUsers = "http://<PATH TO YOUR COMMUNITY WITH ID>/restapi/vc/users/visited?restapi.response_format=json&page_size=1000";
//Get a list of badges of last visited users
static string APIQueryBadges = "<PATH TO YOUR COMMUNITY WITH ID>/restapi/vc/users/id/<USERID>/badges?restapi.response_format=json";

static void Main(string[] args)
        {
            date_start = "2018-03-05";
            date_end = "2018-03-11";
            APIQueryLastVisitedUsers += "&date_start=" + date_start + "&date_end=" + date_end;

            GetUsers().Wait();

            Console.ReadLine();
        }

static async Task<LithiumUser> GetUsers()
        {
            HttpClient client = new HttpClient();
            LithiumUser lithiumUser = new LithiumUser();
            client.BaseAddress = new Uri(APIQueryLastVisitedUsers);
            client.DefaultRequestHeaders.Accept.Clear();
            client.DefaultRequestHeaders.Accept.Add(new MediaTypeWithQualityHeaderValue("application/json"));

            string path = @"E:\EarnedBadges.csv";
            string badgesTitle = "";
            string filecontent = "";
            try
            {
                HttpResponseMessage response = await client.GetAsync(client.BaseAddress.ToString());
                if (response.IsSuccessStatusCode)
                {
                    //get a list of users who visited the site during the specified period
                    lithiumUser = JsonConvert.DeserializeObject<LithiumUser>(await response.Content.ReadAsStringAsync());

                    foreach (var user in lithiumUser.Response.Users.User)
                    {
                        // we will get badges of each user

                        badgesTitle = "";

                        APIQueryBadges = APIQueryBadges.Replace("<USERID>", user.Id.Empty.ToString());

                        response = await client.GetAsync(APIQueryBadges);
                        if (response.IsSuccessStatusCode)
                        {
                            LithiumBadges lithiumBadge = new LithiumBadges();
                            lithiumBadge = JsonConvert.DeserializeObject<LithiumBadges>(await response.Content.ReadAsStringAsync());
                            foreach (var badge in lithiumBadge.Response2.UserBadges.UserBadge)
                            {
                                string[] date_start_arr = date_start.Split('-');
                                string[] date_end_arr = date_end.Split('-');
                                // we need the badges earned only during a specified period
                                if (DateTime.Compare(badge.EarnedDate.Empty.DateTime.Date, new DateTime(Convert.ToInt32(date_start_arr[0]), Convert.ToInt32(date_start_arr[1]), Convert.ToInt32(date_start_arr[2]))) >= 0 &
                                    DateTime.Compare(badge.EarnedDate.Empty.DateTime.Date, new DateTime(Convert.ToInt32(date_end_arr[0]), Convert.ToInt32(date_end_arr[1]), Convert.ToInt32(date_end_arr[2]))) <= 0)
                                {
                                    badgesTitle += badge.Badge.Title.Empty.Trim() + ",";
                                }

                            }
                        }

                        if (badgesTitle!="")
                            filecontent += user.Id.Empty.ToString() + "," + badgesTitle + "\r\n";
                        
                        APIQueryBadges = APIQueryBadges.Replace(user.Id.Empty.ToString(),"<USERID>");
                    }
                    using (StreamWriter sw = File.AppendText(path))
                    {
                        sw.WriteLine(filecontent);
                    }
                    Console.WriteLine(filecontent);
                }


            }
            catch (Exception e)
            {
                // return null;
            }
            return lithiumUser;

        }

This app returns me a CSV file with the following format:

<userId>,<badgetitle>,<badgetitle>,<badgetitle>,...

<userId>,<badgetitle>,<badgetitle>,<badgetitle>,...

I hope it will help someone.