first, i want to say that no accent is weird. all an accent says is that you speak more than one language, which means you are a smart person who has worked hard. and your english is very good, the pronunciation even, and the accent can be advantageous if you teach in the region it originates. you will be able to understand common mistakes in the language, and many are better able to understand foreign languages spoken in their own accent, especially if it is quite foreign.
first, try to figure out which engilsh you want-- american english is still a dialect, like british english is. i'm moving forward as though you want american english, since that sounds the closest to the recording.
have you heard of the international phonetic alphabet? since you're already into languages, it might make more sense to you than most others. it's a system of notation for sounds in different languages. it's more useful to linguists, but the website has a catalog of most every sound from most languages. if you can find which sounds are used in american english, which shouldn't be too difficult, as most english examples are written as such, you can practice copying the sounds.
it sounds like your first language is tonally based, which can actually be of help later on. there are few english words that change meaning on inflection, and the pattern of stressed/unstressed syllables is pretty subtle, and unnoticed by most people. try speaking a few lines in as flat a voice as possible, to make yourself aware of what you instinctively do.
something not many people are aware of is the physical aspect of spoken language, how it resonates in the face and throat. this is where tonal experience can help: work though different vowels and tones, noting where you feel them in the head. almost all american accents take place in the middle-back of the mouth-- picture the sound coming from the lower half of your mouth, a little ways before your tongue meets your throat.
probably one of the best ways to work with accents is look for acting resources on accents. other than that, consuming pop culture and practice are the best thing you can do!
i'm rooting for you!