It might be possible to achieve that effect without creating individual titles, however creating a stack of titles is the easiest and most strait forward way.
Create a finished screen 1st, with all the elements that will appear by the end of a title sequence. Click the "new title based on current title" button to create a copy, then delete the last title element on the page, then repeat until you are just left with the 1st element that you want to appear on screen.
Overlay them on your timeline in reverse order of creation, and you have your effect.
That should be the easiest way.
Create the title with all of the information and then either crop the title using "hold" keyframes so that you can see all of the next line at once instead of seeing the line appear as the crop moves from one place to another.
Here is a sample of how easy it is to use crop on a title. Download the file and look at the way the keyframes look on the title in the Effect Controls Panel.
The video is below and the project file can be downloaded by a right click on this link.