Theoretically, you can do that. But practically, it won't work.
When you license something as open source, you don't necessarily need to license it to everyone. You can choose to only license it to a selected audience.
But any open source license includes an unlimited right to sub-license. That means anyone who receives a copy under the Apache license can sublicense it under the same conditions to anyone they want, including "This Company", and there is nothing you can do against it (not as long as you still want to call your software Open Source and its license the Apache license).
You are of course free to create an own crayon license based on the Apache license which forbids redistribution to "This Company". It's your work and you alone can decide who can use it and for what. But when you make use of your copyright in this way, please do not call it open source.