Use a while loop while the player is online or loop all players in an "every x ticks" statement. These will update whenever you see fit and do not require a player to move.

Example 1 (While Loop)

Code (Skript):

1. on join:
2.     while player is online:
3.         if player's targeted entity is a player:
4.             send action bar "&a%name of player's targeted entity% &7- &c%health of player's targeted entity%/%max health of player's targeted entity%" to player
5.         wait 5 ticks # Action bar will update 4 times a second.

Example 2 (Every x ticks)

Code (Skript):

1. every 5 ticks:
2.     loop all players:
3.         if loop-player's targeted entity is a player:
4.             send action bar "&a%name of loop-player's targeted entity% &7- &c%health of loop-player's targeted entity%/%max health of loop-player's targeted entity%" to loop-player

This is two examples of how you could do this. I have no idea which one is more efficient though.

 

It is less laggier than the "on any move" event I am pretty sure. I think you will be fine though. You can make the ticks higher if you don't want to risk lag. I just used 5 ticks as an example.