If something is shakiest, it is the most likely to move or fall. It is not steady or strong.
The word shakiest makes people think of things that are not safe or reliable.
Examples:
The shakiest part of the bridge is the middle.
Her hands are the shakiest when she's nervous.
The shakiest table in the restaurant wobbles when you touch it.
The shakiest chair in the room is the one with only three legs.
The shakiest tower of blocks fell down first.
The shakiest part of the mountain is the very top.