You can reset your password without mail if you have added your number on Instagram account. If you haven’t added the number. Add the number in your profile.
Now again log in and tap on the forget the password.
Instagram will ask you to fill your phone number in the box.
Put your phone number which you have used for your Instagram account.
Instagram will send a verification code on your number.
Copy the verification code and put it in code box.
Type your new password. Your password has been changed. This is the only way to change the password.