hi CReardon! Well done on getting to the level 5 boss
Firstly, to reassure you, I refreshed myself by looking at that piece, level 5 skill test 'Bach's Bourree', and you could definitely play that with fingerpicking OR using a plectrum. I would urge you to practice both. When I started I only used fingerpicking exclusively, and now I wish I had started with a plectrum earlier so that I would have had longer to develop my picking skills now.
As for the song, there are some advantages to the way it is written that might help to get up to speed with it.
Firstly, as everyone will recommend, definitely slow it right down and play it through as slowly as you need to quite a few times just making sure you are able to sound each note.
An important thing to notice in this song is that the majority if not all of the song is made up of notes from frets 1-5. This may not seem important, but when you look more closely, you only have to finger a couple of notes on fret 1 in the whole song. This means that nearly always, the bottom fret that you will be using is fret 2 (except of course when you play an open string.)
Similar to what ylly has said, because the lowest fret used is nearly always fret 2 (except for like, two notes that are on fret 1) it gives you some options on what positioning to use. It is a preference thing, and I personally find I prefer using second position, (ie. your first finger on fret 2, your second finger on fret 3, your third finger on fret 4, your fourth finger on fret 5). Alternatively as ylly uses, you can use first position, and slide your pinky down a fret to play notes on fret 5.
If you do try second position, as the song is conveniently written like this, for almost all of the song you will not need to move your fretting hand too much at all except to move your index finger back a couple of times from fret 2 to fret 1 to play just a couple of notes.
The main disadvantage of using second position at first, is that you may find it a bit confusing, starting out. It can be confusing at first, because the song will say 2 (fret 2) but you will be using your first finger to play fret 2, or the song will say '4' for example, but you will be using your third finger to play fret 4, and so on. Using different 'positions' is something that you need to get used to though, (resting your index finger on a different fret than fret 1 as the starting position). I guess there are advantages and disadvantages to using both first or second position in this song. What you should definitely do, is practice trying both!
You may have been finding it even more difficult up until now, trying to play each fret as per first position up to fret 4, and then when there is a note on fret 5, you have to move your whole hand, and it could be throwing your rhythm and your hand out a little. After a while, you will get used to just sliding the pinky down and then making sure you are back to your original position for the next notes.
I played it through a couple of times in second position and I found it made a difference. I'm no expert myself unfortunately, so maybe a couple of the advanced players here could give you more in depth advice, but I'd advise you to give that a try.
If you did want a further guide I could always try and post a video just to give you an idea of how I would go about tackling it, but like I say, I'm no expert, so be warned
I hope you manage to get it down! Best of luck
And as always, remember to slow things right down in practice mode