Do I get Kerrigan levels if I replay a mission?

If I am playing the campaign in Hard, and I cannot complete all optional objectives to get the Kerrigan Levels for a specific mission, can I replay it immediately upon finishing it but in Normal to try to complete everything and get them? Or only the first one counts?

If you missed some Kerrigan levels in earlier missions, you absolutely can go to the archives to replay those missions and any additional levels you gain will be counted towards your campaign total.

For example, let's say your current campaign progress is up to the Phantom of the Void mission, but you only received one Kerrigan level from the Waking the Ancient mission (you can get a total of 3 via the bonus objective). You decide to replay the mission via the Archives and manage to get 2 Kerrigan levels out of the 3 that are available, you will gain one additional level to your total (as you already have 1 from the first playthrough). If you want the last level from the mission, you will need to replay the mission again and make sure this time to get all 3 essences in the mission.

There is only one caveat. When you replay a mission, the game will use the Kerrigan level accumulated up to the point of that mission in the campaign. Once you finish the replay and wish to proceed with the campaign again, you will need to go back to the Kerrigan screen and reselect the abilities that were unselected.