Cassandra Cain was arguably DCs' best fighter and still had to earn her worth in combat with Lady Shiva. Let's see how her adopted brothers did and how having certain writers makes all the difference when taking on the woman that's better than Batman.
Nightwing vs. Shiva
In new 52 she's officially the first baddie he fought as Robin and she saw great potential in him. Shiva of course was too much for Batman and him to handle. Years later she encounters Dick as Nightwing and figuring out he was the same person her interests is renewed.
Outcome: Dick gets his ass handed to him which is actually fairly in character since she's the superior fighter. She's still impressed with the fight he gave her since he's suffering from previous injuries. What I don't like is Dick having the ability to read body lanague since that was Cassandra Cains' thing. I also don't like Shiva seeing him as "special" or calling him the nickname she gave Tim. I wouldn't mind her taking interest in Dick if there wasn't for the body reading bit. Shiva always did like testing people and seeing others hone their skills. Tom DeFalco helped Kyle Higgins write the origin of their rivaly and did the actual Shiva/Nightwing battle solo.
(Red) Robin vs. Shiva
Before the relaunch Shiva took an interest in Tim and when Batman disappeared she challenged him to a fight to the death. Tim accepted leading to him getting several bones broken and Shiva collapsing on the spot.
Outcome: While I like most of Fabian Niciezas' work as a writer his Red Robin stuff made Tim seem far too perfect. The reason Shiva is taken out so easily is because Tim planned ahead to poison her before the battle. While this is in character and a smart way to defeat her I still have a problem with it. That problem being Tim just assuming she'd eat something, basing his entire plan around it and it working out. If he knew she liked a particular food this would work better for me but as it is it comes across as dumb luck. You'd also think Shiva would be more careful with people wanting her dead all the time since she is a top assassin.
Red Hood vs. Shiva
In the old canon Jason met Shiva as Robin during Death in the Family. Most of the fight was between Batman and her. Jason only has two parts in said fight. First being dazed as Shiva starts the battle then coming up behind to attack which distracts her from Batman. That's it. Writer James Tynion the Fourth has changed Jasons' previous established relauched training backstory to make Jason a student of Shiva. (Complete with her knowing his real name.) They fight and this is the entire battle.
Overall: I think Jason ranks pretty high on skill since he was able to take on Batman, Nightwing, and Green Arrow in the last canon. But this is pathetic and hardly does anything for either character. I can't even call this a battle and it's more insulting because it has everyone acting like Ra's Al Ghul is the superior fighter. No, he's not and that's never been the case. Yes he got a power up in the arc but Jason himself says he'd never have a chance to defeat him in a sword fight which is B.S. Both characters deserve better. Jasons' been shown to be smart enough to fight like Tim did above without guessing the outcome. But this "shortcut" is as lazy as Tim defeating Cassandra Cain because he didn't use a fighting style or Talia defeating Shiva with a chair.
How Lady Shiva should be written?: Shiva should have a real interest in Batmans' students and seeing if they reach their potential. She's a teacher and takes pleasure in testing those that catch her eye. If they defeat her it shouldn't be a easy battle, in fact it should be one of the hardest fights these former sidekicks ever have. If they win by pure skill in hand to hand combat it should be built up through varies issues. In most cases it should be because they manage to outsmart her. The usual outcome is that she will defeat them then move on after offering some advice. Shiva IS the best fighter on the planet unless Cassandra Cain is around or someone takes her out. That's why she's hired and that's what makes her such a big threat. Downplaying that doesn't make the other character look more badass. If you want to see it done right look at Cassandra Cains' Batgirl run.