The following translatable text will be used:

achievement.openInventory.desc = Press '%1$s' to open your inventory.

To insert text in place of the argument (%1$s), the "with" list-tag must be used. For example, a working command:

/tellraw @a {
	translate:"achievement.openInventory.desc",
	with:[
		{
			text:"TEST",
			color:gold
		}
	]
}

Result: "Press 'TEST' to open your inventory."

However, using the new "selector" tag will not provide the player's name, and instead displays the selector itself:

/tellraw @a {
	translate:"achievement.openInventory.desc",
	with:[
		{
			selector:"@p",
			color:gold
		}
	]
}

Result: "Press '@p' to open your inventory."

Changing the "with" to "extra" will properly display the player's name at the end of the text, showing that the selector works correctly elsewhere:

/tellraw @a {
	translate:"achievement.openInventory.desc",
	extra:[
		{
			selector:"@p",
			color:gold
		}
	]
}

Result: "Press '' to open your inventory.Skylinerw"