I want to learn how to talk like that (i.e. sound like a native speaker when I am not).
As you speak English, pay attention to where exactly your voice is resonating in your mouth. Visualize it, if that helps.
British received pronunciation -what many people outside the UK call a "British accent", though that's not really accurate- resonates far forward, in the front of the mouth. If you push your own voice forward, you'll get something that sounds very similar; it just sort of falls out naturally. If you pull it all the way toward the back of your mouth, you'll get something very like a Slavic accent. Obviously you're not going to completely pass gor British or Serbian just by doing this -there are ither things like diction to consider- but you might be surprised at how far it can go. Experiment with this; push your voice around and see where it goes.
There is also an American received pronunciation: what you hear newscasters speaking, among other things. As with the British, this is often considered by outsiders to be an "American accent", but again, that's not strictly accurate. If you want to do this, hold your voice in the middle of your mouth, maybe just a tiny bit forward of the center. Again, this isn't everything there is to an American accent. But you may fibd that it helps a lot.
I looked her up on YouTube, her accent was pretty apparent, checked the top comments, and they were also about her accent. They liked her accent, it's not a bad thing, but she definitely has an accent.
If you want to get an accent like Heidi Klum, good luck.
Only real Germans can pull that off.
And as someone who tries to improve his spoken English with each passing day, I have to tell you that there always seems some kraut stuck on your accent.
You can learn to speak like a kraut, but I tell you it's gonna be damn hard, and especially as an English native speaker you are going to have a hard time. Kiss goodbye "th", you gotta learn "ch". And then try to speak normal English while sounding like a kraut.