What type of wall is this?
Behind the plasterboard (drywall) it looks like it could be the metal of either  an RSJ or a Catnic. Either could have been used to support the brickwork over the window aperature. If it's a Catnic, it'll be possible to drill through, and use self-tappers to secure the blinds. If it's an RSJ, the steel will be quite thick, and will take a long while to drill holes for screws.
A drilled Catnic could have a larger hole through which you could push a drywall fitting - a longer one, so it expanded on the other side of the thin steel.
If it's an RSJ, there's also the possibility of drilling and tapping, so a bolt can be threaded into it. A very strong fixing, but maybe beyond diy.
You may be better off trying to fix into the sides of the reveal - at the very top, which may just be drywall - but needs a different blind fixture.