@Dan.phi, with Plots.jl you often need to be creative and it will rarely disappoint.
using LaTeXStrings, Plots; gr()
y1, y2 = rand(100), rand(100)
histogram(y1, ylims = (0,50), label = L"\left\Vert\beta_{1}^{2}-\beta_{2}^{2}\right\Vert")
scatter!([minimum(y1)],[0], label=" ", ms=0, mc=:white, msc=:white)
histogram!(y2, label = L"\left\Vert\beta_{2}^{2}-\beta_{3}^{2}\right\Vert", legendfontsize=10)
NB: nevertheless, your code produces a legend that is perfectly legible in Julia 1.6.1, Win 10, Plots v1.16.3, gr backend
