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Put nine +1/+1 counters on target land you control. It becomes a legendary 0/0 Elemental creature with haste named Vitu-Ghazi. It's still a land.
trigger the ability of Kiora, Behemoth Beckoner?
Whenever a creature with power 4 or greater enters the battlefield under your control, draw a card.
It doesn't trigger.
It's not simply a question of checking if the state of the game went from not having a creature of power 4 or greater on the battlefield to having one.
An object only enters the battlefield when it moves from a zone other than the battlefield (e.g. hand, graveyard, exile) to the battlefield or when it's otherwise created on the battlefield.
Enters the Battlefield
A nontoken permanent “enters the battlefield” when it’s moved onto the battlefield from another zone. A token “enters the battlefield” when it’s created. See rules 403.3, 603.6a, 603.6d, and 614.12.
Since the land in question already existed, and since the land in question was already on the battlefield, no object entered the battlefield (much less one that was a creature with power 4 or greater). As such, the ability isn't triggered.
A ruling on Kiora, Behemoth Beckoner reminds you of this:
However, you can’t have a creature with power 3 or less enter the battlefield, raise its power with a spell, an activated ability, or a triggered ability, and have Kiora’s ability trigger.
No. When an object changes type, it does not "enter the battlefield". Note also that the rulings page for Kiora explicitly says:
However, you can’t have a creature with power 3 or less enter the battlefield, raise its power with a spell, an activated ability, or a triggered ability, and have Kiora’s ability trigger.
While this is not the exact situation you are describing, it is functionally equivalent. In both cases, and object starts out as not "a creature with power 4 or greater" and later becomes one.
No, it doesn't. The land you target with Awakening of Vitu-Ghazi is already on the battlefield, so it doesn't cause any enter-the-battlefield effects like Kiora's.
