Hi guys, I'm so grateful for these replies.
First of all, I am not a native speaker nor a teacher. I learned English as a child and have a wee bit of accent which Americans would assume British, and Brits would say Australian. I don't realise myself but it is a bit confusing sometimes, so I'd just smile whenever I was told.
Thais have a very thick accent which they mispronounce "L" "R" "W" "V" and "TH" sounds. Since I have been living in Thailand for 5 years already, I have no problems with their way of speaking English. I think if she was in the states or UK, she'd not be easily understood with her accent, and that is where I come in to fix.
I and my student had a brief lesson today, where we practised, "L" and "R". By the way, my student's reading skill is decent although I have not checked her writing yet. I suppose she is well exposed to native speakers since she is married to one, thus, always being around them.
I plan to work on phonetics, sentence intonations, consonant and colloquial expressions with her.
ThePersar, thank you so much for your excellent suggestion. I am definitely checking out the book you recommended, along with other work books.
AlexAD, you have raised an interesting question. I think having an accent makes you a more interesting person as long as it is easily understood. I do not personally care and a lot of my native speaker friends admit that they find a person, with a little bit of accent, more interesting.
However, when it comes to landing at a good job, being a leader in a social group, or whatever their personal reasons are, at least once in a life, they want to get rid of their heavy unnatural native accent. I do not think I can ever fix my student's accent and I will not try because it is nearly impossible for her. Nonetheless, my job is to correct her mispronunciation, well, that's why I am hired. I have to put every effort to help her.