The PishiWiki gives a pretty good explanation of what she's capable of:
http://ikusat.mac.org/mbac/index.php/KohakuPeople don't normally play Kohaku solo, as she gains so much more when played as a team(awesome 214B Hisui assist as a blockstring ender, another overhead option with 214C). However, Kohaku does gain a fairly formidable anti-air, which is shield(EX or regular, it doesn't matter, though if it's EX, you're better off doing 5A and then doing an aircombo), and then XX command throw. The XX means you delay for a bit, as if you do the command throw too early after the shield, it'll come out before the opponent lands, making it whiff. The other thing solo Kohaku gains is 214A/B, which were pretty useless pre-Ver.B, but have a fairly specific use now. Basically, 214A/B now allows you to move in the air after you do it, so a practical application for this is when you have your opponent trapped in the corner with a plant setup, you do 214A/B, and after the move is over, you can do a basic high/low mixup by doing airdash j.B/j.C, landing and doing 2A, or doing an empty airdash into whatever. The explosion from the move partially covers up Kohaku, making it difficult for your opponent to tell what you're gonna do.
I'd also like to add that 22B can also be used midscreen, or anywhere outside of corner, though it's not as strong obviously. When not in corner, your opponent now has the option to safely get away by backdashing or jumping away, but you can definitely punish each option. For backdashing, what you can do after setting up the plant is do 2A for the low hit, and if the opponent backdashes, quickly empty cancel 2A into 2C to tag them. Dashing up and ground throwing also works against some character. To take care of opponents that try to jump away, you can dash up and do 5B or airthrow them.
When ending a ground combo into 22C(like 2C 236C 22C) midscreen, it's pretty standard now to superjump over them with j.C, and after you land behind the opponent, you can do the standard high/low with 2A or instant j.C. What I've also seen recently is walking towards the opponent and then doing Kohaku's dodge(2A+B/2Q), which crosses up the opponent, making them eat the cactus if they don't block the right way.