This page explains how to recruit Draggy in Chrono Cross: The Radical Dreamers Edition.
Draggy is a baby dragon, possibly the last of its kind (poor thing).
How to Recruit
You can recruit Draggy after the events of Fort Dragonia and returning to Home World as Lynx.
Where to Find the Big Egg
Beforehand, you need to obtain the Big Egg from Fossil Valley in Another World. If you missed it, there’s a rope ladder halfway along the path. After climbing up, descend the vertebrae ladder towards the left. If a soldier stops you, ignore them; otherwise, you may need to return slightly later.
From there, grab the massive egg in the nest. A Dodo will become aggravated and try to attack you–feel free to defeat it or run.
What to do with the Big Egg
Later on, after borrowing a boat from Norris, sail to Mt. Pyre Shore in Home World and pass through the tunnel, to reach this world’s Fort Dragonia. Inside, deactivate the four obelisks on the ground floor, like in Another World. The puzzles are the same, but there are no bosses.
After the central column appears, deactivate the 5th obelisk to bring down the elevator. Now use the elevator to go down. You’ll be taken to an incubator room. Go down to the middle incubator, which is the only one that works. Then place the Big Egg there via the key items menu.
Draggy will almost instantly hatch from the egg. Afterwards, agree to help search for its parents. If you don’t, we’re not sure where Draggy goes…