I think you can do it alone and you have to buy the train ticket one day early. There is bullet train at Beijing North Railway Station (Xizhimen) to Badaling, in one hour at 8am in the morning. The advantage for you to participate in a tour is that you can save time and visit other places in the same day without considering the transportation problem. I found some Beijing one-day tours(https://www.travelchinaguide.com/package/beijing-one-day-tours.htm) is cheap and nice in this website.