How to do The Hole and the Ocean on iOS with no keyboard

Chrono Trigger for iOS does not 'sync' to iCloud in the way you are hoping.

I've played on my phone and seen that the save game does not sync my iPad.

To check for other games/apps (if you own them) look under Settings > iCloud > Storage & Backup > Manage Storage.

The apps listed under 'Documents & Data' sync between devices.

The apps listed under your device's name are backed up, but not synced via iCloud unless they are also in the previously mentioned list.

Some games/apps sync using cloud servers other than iCloud (Eg: Dropbox). In this case, they would appear in the back-up list, but not the Documents & Data list, but would still be syncing.

Chrono Trigger isn't one of those.

You could restore from a backup and thus transfer your save game to a different device, but that isn't the situation you're describing.

You need the sponge.

You can get it by jumping in the ocean.