Edit: I have fixed this issue! You can find the full solution here.
An extremely jarring outline and shape of the branch is formed behind the leaf textures and I tried as many things as I could and this problem was so specific whenever I tried looking up solutions it came up with nothing.
If it helps, I used CG Geeks 1 minute low poly tree tutorial and used a Shadeless texture setting since the normal one had an ugly slightly darker side of each texture.
Please help!
Thanks.