lulu.doll -- For breathability, natural fibres (e.g. cotton) are usually a good bet -- I've worn five layers of cotton and silk, including a couple heavy ones, and been fairly comfortable in a hot summer. That said, for the top I'd suggest looking for a mid- to heavyweight cotton sateen; it'll give you some of the sheen in that image without being really shiny, and while it looks substantial it breathes rather well. If you really don't want any sheen, consider a cotton twill. (That top's a slightly odd colour, but you could dye cottons if you wanted to.) You could also consider layering a wicking undershirt beneath it to help with sweat.
(Yuuzuki_x -- I can't load videos or I'd try to help; do you have any screenshots or stills?)
Therese von Ludowing (Sound Horizon's Märchen)Elsewhere: Journal ~ ACP ~ CosplayLab
Catelyn Stark (A Song of Ice and Fire / Game of Thrones)
Elisabeth - red ballgown (Elisabeth - Takarazuka version)
Thessaly (Sandman - The Kindly Ones)