How can I achieve this light blue glow effect over text in Illustrator?
To add the soft glows and highlights, Gradient Meshes would probably be a good option if Illustrator must be used.
It just takes a few small meshes to create the highlights.
(This is NOT perfect and is only included to show the methodology.)
...Meshes with transparent edges then a light blue center.
The outer glows are created by applying the
Offset Effect to additional fills. If I were strictly interested in only non-raster objects, I'd create the outer glow/shadow with a mesh as well.
The large dark blue stroke has shadows in it, I'd apply those with small meshes the same way the white highlights are created.