I need a lot of help going Red (Pictures inside)

I've been dying my hair for years but my natural hair color is an ashy brown with a bit of red mixed in. I decided to go dark brown a few years and I absolutely hated it. In attempting to fix it, my hair got pretty fried in the process. I let it rest for about a year and a half and then my sister used demi-permanent to try to make it red. It didn't really work, just sort of tinted it. That was about 4 months ago. perhaps a bit more.

She wants to try demi again tomorrow but I have a feeling it won't do much good. Do I need to totally lighten my hair to get my desired color? It doesn't need to be an exact match to my desired red but I don't want a dark red. I prefer something lighter.

What is your advice? What do you think I need to do to get the color that I want? Can I achieve something at least similar with demi dye? My sister works at a salon so she has stuff at her disposal but I really don't want to damage my hair again =/ I'd appreciate any and all help! Thank you.

Here is what my current color is: (Not a very good picture but the best I have)





This is the color that I want:

Thanks! What do you suggest I lighten it with? I'm hesitant to bleach it if I don't have to =/ Is there anything less harsh that can lighten it up a bit? I'm pretty clueless when it comes to this stuff.

Thanks for all your help! I really appreciate it.

Hmm...I'm not exactly sure if there's color in my hair right now, to be honest. My sister used demi permanent on my hair about 4 months ago or so but that would've washed out by now, right? Like I said, I'm pretty clueless about this stuff.

That L'Oreal stuff looks promising...I'm a little afraid to use it but I'll definitely look into it.