The phrase "badly scared" is correct and can be used in written English.
It is commonly used to describe a state of intense fear or anxiety. Example: "The child was badly scared after watching a horror movie."
I'd been badly scared by my TV set.
It hurt pretty badly, but I had decided when the pubes first started coming in that I'd never shave, too badly scared by the old "it'll grow back thicker" adage.
If you're somebody who gets easily scared in horror movies/themes, then you may just end up getting badly scared and not enjoying yourself at all.
When Ms. Styron was young, he told her humorless stories intended to badly scare her: about a homicidal maniac who would store his victims' remains in their house, about (false) plans to sell her pony to the glue factory.
How upset you are afterwards will depend on how badly injured or scared after the attack you were.
The film was Fox's "Elektra," starring Jennifer Garner as the title fighter, and the release bombed so badly that it apparently scared off at least one Marvel executive from giving another superpowered woman the solo spotlight.
The prolonged, enervating battle for health reform, using a badly flawed bill, has scared off both conservative and liberal Democrats in both houses.
Was her father a drunk and beat her so badly that she is scared of guys?
Andy winds up being scared by how badly she's behaving, though of course she never does anything really bad.
The Yankees' eventual 8 4 win was blessedly undramatic, thanks to their stifling bullpen, and the cheering from the sold-out stands was almost forgiving toward the Twins, who had scared us so badly at the start.
