Variables are public by default, so you just have to use get_node to access the node, and then add a dot and then the variable name. You can see my post here for getting nodes.
https://godotforums.org/discussion/comment/30926/#Comment_30926
You can do something like this:
onready var playerNode = get_node("/root/Scene/Node2D/Player_Node")
Then later, read or alter the level variable:
playerNode.level += 1
print("level: ", playerNode.level)
Make sure you access the variable through the node, so it is actually updated. If you just save the level in a variable, that becomes a new integer variable (not associated with the player node) and when you add to it, you are only adding to the copy, not the original value.
Hope that helps.