Heart of the Swarm Campaign- Zeras Achievements: Supreme

Normal Difficulty:

Supreme (10): Win.

Endangered Species (10): Kill 500 of the enemy units in this mission with Kerrigan's attacks and abilities.  The longer your fights with Kraith and Silvan take, the easier this becomes -particularly with Silvan if you abuse Psionic Shift.  If you restrict Sarah's actions to Mend, you won't manage this, though, so take advantage of her offensive abilities whenever you don't absolutely have to save for Mending.  Do keep in mind that her basic attack is still ranged, as well, which leaves her able to strike when you wouldn't normally think so- and when she wouldn't have been able to, prior to Heart of the Swarm.

Queen of the Jungle (10): Complete the mission without Kerrigan ever dropping below 100 life.  Curiously, the greatest obstacle to this is not any of the later fights, nor is it any of the sections where Sarah wanders off on her own to collect an artifact.  Instead, it is the first pack leader, Yagdra.  The final attack it lays out, a constant stream of flaming matter, deals such high continuous damage that it will often force Sarah's life bar into the red and mandate that you use a combination of Mend and Leaping Strike to deal with the beast.  Using Mend preemptively can save you the loss of life necessary to break this achievement, but you have to time it carefully or you will either wind up wasting some of the healing and going red anyways, or hitting Mend too late and having it not matter.

Hard Difficulty:

Whose Queen Reigns Supreme (10): Complete the mission in less than 12 minutes.  This is a very challenging achievement, and should not be attempted on your first play of the mission in a given campaign.  In order to achieve this, you're going to need to go straight for each pack leader, and ignore not only the side groups of enemies but also the Xel'naga artifacts.  The main obstacle here is the sheer amount of traveling you need to perform to get to each location, so any combat time you can cut out is good- there are several groups of enemies that are effectively patrolling rather than attacking which you may be able to burrow and let past, and it's surprisingly possible to more or less 'sneak' Kerrigan by many of the enemies while leaving your troops behind- though this is not at all advisable for dealing with Silvan and Zurvan, for whom you badly need both the ability to spread out incoming damage and the increased overall firepower (respectively).  This is really a very good challenge achievement for mission replays.