Hola mucho gusto soy Hispanohablante una tecnica muy útil usada desde que los niños aprender a hablar español es escuchar varios audios e intentar decir la palabra gesticulando correctamente pero mordiendo un lapiz intentando pronunciarlas

Estoy de acuerdo con Alejandro practicar con un nativo que corrija los errores es lo mejor

The main things that an English native speaker must pay attention to when it comes to Spanish pronunciation are the vowels (specially when they form a diphthong, and specially "eu") , the alveolar flap (soft r) and the plosives like "p" or "t". Given that you are already a fluent speaker, keep in mind that would be more difficult to undo bad habits. However, you could benefit from a native speaker that is able to pinpoint your mistakes, and repeat after you with the correct pronunciation. Then, he could repeat both (your incorrectly pronounced word, and the correctly pronounced one), and see if you can tell the difference. If you can recognize the correct sound, is a matter of practicing producing it. 

¿Hay algun libro que enseñe la mejor manera de reducir al acento de un lusoparlante como yo?