There are three factors that will decide of your overall rank at the end of a mission. Your Style Points, the time it took to complete the mission and the percentage of collectibles found. Obviously, the level has to be completed in the shortest amount of time. Finding all the collectibles is also highly suggested. The hardest part though, is to earn a big amount of Style Points. It's also what will most likely decide of your overall rank at the end of a mission. The best way to rack up points is to use as many different combos as possible. The Trinity Smash is an extremely powerful combo that gives a lot of style points (Rebellion + Pause Arbiter + ). I'd suggest using this ability when only a few enemies are remaining. It's a very slow attack, you don't want other enemies to hit you while you perform it. The Tremor attack (Arbiter + ) is also very good to hit many lined up enemies at the same time. Another combo that greatly helps me to rack up a lot of points is the combination of the Buy In and the Eryx Stomp (Aquila + pause + ) + (Double Jump + Eryx ). Other great combo -> Buy In, Killer and Cleaver (Aquila + Pause + ) + (Aquila + + + ) + (Osiris + + Pause + + ).
If you go in Select Missions, you can see the rank you already achieved on every mission.