At least in Origins.
The Initiation DLC promises a rematch against Lady Shiva as well as insight into Bruce Wayne's early days of training. Unfortunately, this promising extra is little more than a series of Challenge Rooms followed by a Boss fight. The story, such as it is, is little more than a series of cut-scenes of Bruce's ninja master talking about how worthless the future Batman is before trying to get him killed.
The premise of the DLC is Bruce Wayne has gone to a remote mountaintop monastery in order to learn the ways of the ninja. Master Kirigi is insulting to Bruce throughout the campaign, saying he doesn't respect the latter's refusal to kill and showing a racist disregard for him throughout. Bruce, himself, never speaks during the DLC but just stands there respectfully the entire time.
|If only the DLC was half-as-good as this picture.|
Another complaint about the DLC is that it's actually difficult to find. It's not located on the main menu but the challenge maps and it took me awhile to track it down. The skins for Bruce Wayne as a trainee and a ninja are useful but I'm not sure I'm going to get much use out of them.
In conclusion, Initiation is not worth buying. The Challenge Rooms aren't even that fun and the final boss fight with Lady Shiva takes forever to get to. Save your money and play around in the Challenge Rooms the game provides for free.