How can Final Fantasy 14 Chocobo 10 be upgraded to 1 1?

After reaching the upper limit of grade (grade and experience show yellow)

Put the birds in the bird shed in the guild or individual room.

Feed a tavona onion. Grow it yourself or buy it on the market board.

The upper limit is raised, and the upgrade can be continued.

Feed another one every time you reach the upper limit. Up to level 20.

It's a waste to feed onions before reaching the limit.