Dunno if this needs a spoiler alert but here you go.
I have a 'strategy' for this but it's difficult to figure out without a picture myself, so I went on a dungeon run and happened to get the same picture as you :P
Mine's a tad different, but it started out like this:
So, if you refer to the picture at the top and match all the piece you have, you'll find that the missing piece should end up in the bottom right corner. So we'll start with the piece farthest away from it, the top left corner. Find the the top left piece (the top of the wing in this case) and do whatever you need in order to get it in its proper spot.
As you can see, I have 'slid' the proper piece over to the top left corner. (Forgive my sloppy outlining xD)
Now, you'll want to get a piece next to it into its proper position. And by that, I mean, the piece that should either be directly to the right or directly below the top left corner piece.
For this, I picked the one that's supposed to be directly to the right, the half-wing, half head piece:
... And I moved it around so it's in its proper place next to the corner, as you can see here. You shouldn't have a problem doing this without moving the corner piece.
Now, as you can see, I have two-thirds of the row in place, and now I'm going to finish up the row by putting the top right corner in place next to the two I already finished. The piece I'm looking for is the head/sun piece, shown below:
Now getting this piece in the right place is going to be a challenge, because you don't want to displace the pieces you've already fixed. If the piece you want isn't already in its proper column or the column of the middle piece, you'll want to get it there. Since that was kind of confusing, here's a picture:
You want to get that head/sun piece anywhere inside that red rectangle.
Those six tiles, or rather, that area, is important. For this step, do NOT move any of the tiles already in that area out of that area, and make sure the blank spot is in there, or you won't be able to move anything xD
Great, so this is the hard to explain part. You want to line up two specific tiles: the middle wing/head piece and the head/sun piece so that they are next to each other, in a certain way that once you move them up to the top row, they will be in their proper positions. If you want me to clarify this part, let me know.
Imagine that you rotate all six tiles clockwise in that boxed area. If I did so, my puzzle would now look like this:
So in your head, think of how the two tiles would have to line up in order to be in their proper positions when you rotate them clockwise. Then, try to align them that way, without moving any of the tiles out of the red box. I'll show my steps to make it less confusing xD
*pants* And now we've finished the top row!
But wait, there's more...
You now have to *drumroll please* do the same for the leftmost column!
*groans from the audience*
Don't worry, it's exactly the same technique you used for the the top row, and you should have no trouble getting the tile right below your top left piece into place without disturbing the top row.
But now your 'special box' is here:
And I'm not going to show my steps for this one, since I'm exhausted xD
But when you're done, you should get something like this:
And from there it's a simple matter to move around the three remaining pieces to where they should be!
Oh dear, I should make a guide for this...
Hope it helped! Let me know if you have any questions...
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