A program.cs for a simple console application that shows the version history for a listitem form a SharePoint Online list. This code comes from a simple test application and needs some rework to get a better performance.

GetSPOVersionHistory.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Security;
using Microsoft.SharePoint.Client;

namespace VersioningTester
{
    class Program
    {
        static void Main(string[] args)
        {
            var url = "https://{tenant}.sharepoint.com/sites/my-tester";
            var user = "admin@{tenant}.onmicrosoft.com";
            var pw = "<put the correct password here>";

            var password = new SecureString();
            foreach (char c in pw.ToCharArray()) password.AppendChar(c);

            using (var ctx = new ClientContext(url))
            {
                ctx.Credentials = new SharePointOnlineCredentials(user, password);

                // get v5.0 and higher
                int fromVersionId = 512 * 5;

                Web web = ctx.Web;
                List list = web.Lists.GetByTitle("Index Fields");
                ListItem item = list.GetItemById(1);
                ctx.Load(web);
                ctx.Load(list, l => l.Fields);
                ctx.Load(item, i => i.Versions.Where(v => v.VersionId >= fromVersionId));
                ctx.ExecuteQueryRetry();

                FieldCollection fields = list.Fields;

                ListItemVersionCollection versions = item.Versions;

                // versions[0] is the current version
                // versions[n] is a older version
                // the last one is the version, we need to compare the changes to
                // iterate from n-1 to 0

                int n = versions.Count - 1;

                for (int i = n - 1; i >= 0; i--)
                {
                    string versionNumber = versions[i].VersionLabel;

                    Console.ForegroundColor = ConsoleColor.Magenta;
                    Console.WriteLine("Version: {0}", versionNumber);
                    Console.ResetColor();

                    ListItemVersion workingVersion = versions[i];
                    ListItemVersion compareToVersion = versions[i + 1];

                    Dictionary<string, object> workingVersionFields = workingVersion.FieldValues;
                    Dictionary<string, object> compareToVersionFields = compareToVersion.FieldValues;

                    using (Dictionary<string, object>.Enumerator e = workingVersionFields.GetEnumerator())
                    {
                        while (e.MoveNext())
                        {
                            string fieldName = e.Current.Key;

                            Field field = fields.GetFieldByInternalName(fieldName);

                            if ((field != null) && (field.Hidden == false))
                            {
                                if (compareToVersionFields.ContainsKey(fieldName) == true)
                                {
                                    object currentValue = e.Current.Value;
                                    object oldValue = compareToVersionFields[fieldName];

                                    if ((currentValue != null) && (oldValue != null))
                                    {
                                        if (currentValue.ToString() != oldValue.ToString())
                                        {
                                            Console.WriteLine("{0} :  {1}", fieldName, currentValue.ToString());
                                        }
                                    }
                                    else if ((currentValue == null) && (oldValue != null))
                                    {
                                        Console.WriteLine("{0} :  ", fieldName);
                                    }
                                    else if ((currentValue != null) && (oldValue == null))
                                    {
                                        Console.WriteLine("{0} :  {1}", fieldName, currentValue.ToString());
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
    }
}