Make your 30 min presentation about showing progress on the things these folks care about. You'll have to determine exactly what those things are, but if they're a marketing dept you can be sure money and customer satisfaction are on the list. Don't get into technical details about how you did something, just tell them what you did, what it cost (in time or money), and why it was a good thing to do.
Talk to them about numbers of new and closed tickets, and how you're preventing repeat tickets for the same issue. Show them that progress is being made on long-term efforts such as a planned hardware upgrade or new application roll-out.
For long-term work you need to announce expected milestone dates up ahead, then report that you met those dates. If you think you're going to miss a date, say so well before you actually miss it, explain what happened, and announce the new date. If you think you might make the date but you're not sure, just announce that it's "at risk", then say what you're doing to try to bring it in on time. If those efforts don't bring things back on schedule, announce that the date will not be met.
If you just let the date pass without comment it looks like you either forgot about the deadline or you're trying to hide a mistake. Either way is unprofessional and disrespectful of people who are relying on your work to do their own. If you're up front about it at least you give other people a heads-up in time for them to adjust their own schedules.
If they're asking for more "data", find out what they mean by "data". If these are marketing people they might be looking for cost analysis, or explanation about how the work benefits existing customers or helps drive new sales.
30 min every day sounds excessive for a status update. I'd see about getting that down to 30 min once or twice per week. The only way daily updates makes sense to me is if they really do want you to walk them through technical details, or if you're reporting on a large volume of work done by staff who report through you. If there are open critical issues maybe those should be reported daily, but I'd think you could get through that in 5 minutes, then get back to actually fixing them.
Also, see if you can get them to accept a written status report instead of verbal. It may seem like more work at first, but it's not really once you've done a few. If they go for that, make the report look "professional", but not a marketing brochure or a doctoral dissertation. Format it so someone can scan it quickly and get the main points right away, then drill down for more detail on certain items they really care about. Guidelines for Resumes might help with this part.
A chart showing decreases in defect counts or ticket turnaround times could be helpful. Obviously you want decrease in these numbers, but if you get an increase report that too, but be ready to explain the cause and tell how you're working to get the numbers back down. Categorize the different kinds of issues you work on and reporting separate counts/trends for the different categories.
A selling point of the written report is that you have a record of what was said for future reference. That is, if there are questions about an up-tick in a certain kind of ticket, you might be able to look back and show that the same thing happened the last two times you upgraded a certain app, that it was a temporary blip, and how long it took to get back to normal.
This might not replace a verbal update altogether, but you could limit the verbal update to high-priority issues, places where you need to bring in extra help, notification of starts or ends of major efforts, etc.
Also, tell them not only what you've completed, but what's coming next, and if possible when you expect the new items to finish. For example, if you said in this week's report that you're going to be upgrading a certain server next week, next week you should report that that was done, or explain why not. Over time you can show how you're planning your activities and following through on your plans in a timely manner.
EDIT: Reading the question again I think I may have misunderstood. Are they asking you to provide an accounting of what you were working on during each 30min period during the day? Or are they asking for a 30 min report on what you did during the whole day?
If they want "time accounting" in 30 min increments you can probably find some freeware to help track that. I don't use one myself, but I've heard of simple apps that are basically "stopwatches". You can set up timers for different tasks, and switch between them with a single click. They're mostly meant for tracking billable hours, but that almost seems like what they're asking for.