Listening and note-taking at the same time can be quite a challenging task. In order to do this, I advise to use the following strategies.
Firstly, it is important to already have a rough understanding of the content that you are going to listen to. Knowing the context of what you are going to hear is going to be very helpful when it comes to deciding what is important to note down and what can be left out. If you do not have this context, note-taking can be quite challenging, as it can make the initial filtering of information difficult. However, you can go back over your notes to decide which pieces of information are relevant afterwards. You can then edit your notes accordingly, to highlight key information.
Secondly, in order to not miss out on further important facts, it is important to write in short phrases. Writing in full sentences will take far too long and will lead to further important information being missed. It can be quite challenging to keep up with the speaker, especially if they speak very fast. If possible, taking pictures of a live presentation or screenshots of a video can save valuable time and will instead allow you to focus on what is being said.
Lastly, another important listening and note-taking skill is to listen out for vocal cues from the speaker. A speaker will often raise their voice, change their intonation, or speak a bit more slowly whenever they want to stress or emphasize something. They might even repeat key information several times in order to stress their importance. Being able to notice these audible cues will help massively with note-taking, as it highlights clearly which pieces of information need to be written down.