A few reasons why your cover doesn't sound like the original: (I'm considering just the parts before the vocals)
- The first background crazy sound is very different (but I don't think this is critical)
- In the intro there are 2 violins, you version has only one. If my ear isn't tricking me, the higher one (that you correctly reproduced) goes F# G# A, A G# A....; and the lower one would be around C# C# D, E E F#. (please check this and transpose accordingly!). Then when it goes super high I think there are 3 violins.
- The drums are a lot different. As said in the comments, the original has straight sixteenths on the kick drum, and quarter notes on the snare. You version has alternating kick drum and snare, and sudden changes in rhythm that I didn't quite understand.
- You lead guitar has way too much reverb. The notes sound correct though.
- There is no rhythm guitar in your version. The original does straight sixteenths too, and plays the root of the chords, that are F#m | F#m | D | E... (one chord per bar, each bar has 32 notes).
- Your version has no bass too. It is not very noticeable in the original, probably because it just follows the rhythm guitar.
- The piano is incomplete. You got the top notes, but it actually does arpeggios in sixteenths, starting on top and going down probably doing the same chords I said above.
As you can see, the problem is not converting the vocal line into guitar. Anyway, this was just to give you some guidance, but since specific transcriptions are off topic, here comes the real answer.
Before trying to transcribe the whole song, focus on one part at a time. As @ggcg stated in the comments, each further part will become easier. So, listen to the violins, try to figure out that second violin I talked about, check what's different and why. Is there another violin missing? Is one of the voices wrong?
Then move to the first bar of the metal part. Listen to it over and over, try to hear every aspect and every instrument. Work on it until it sound just the same. Is is too slow? Are there missing notes? Why does it sound incomplete? All the work you do here will be reused in further bars.
Things that can help you have also been cited in the comments, for example looking for sheets or tabs. Of course you must check because they are often wrong, but they will give you guidance and help you filter the different instruments and voices.
The more you try to do this, the more natural and easier it becomes.