Venus Winter's Run Strike Mission consists of three parts, infiltrating the enemy base, clearing out all hostiles and killing the main boss, Aksor the Archon Priest.
Get into the enemy zone like in Winter's Scourge from the Ember Caves. Reach the Winter's Lair, which is a Darkness Zone, you will find Vex and Fallen fighting here.
Try to fight all the enemies on your way focusing primarily on the Hydra. Take part or ignore the Fallen and Vex fight, taking part will help you gain more experience.Then advance to the Cinders.
Since you will be on the cliff, try to eliminate the Fallen and Vex by taking advantage of this height. After the battle, deploy a Ghost to open the hatch, and be ready for three waves.
These waves will have Goblins, Major Minotaur, Major Hobgoblins and two Major Hydras with Harpies. Use Super Abilities for clearing these waves. The Hatch will open after the waves are over. Reach four Pikes, which are Sparrows with weapons, and use them to travel through the Ash Coves.
You are likely to meet two Major Hydras, kill them using Pikes and advance to the Winter's Run. Now you will encounter more Vex and Fallen battles,but this time along with a Major Captain. After destroying the last enemy, free the Aksor from prison cell.
Aksor is an Ultra Captain with no shield but a huge health. He will use Shrapnel Launcher against you, so do not be in the open for longer. The weak spot for Aksor, is his head, make it your prime focus. Use Heavy Weapons and Super Abilities when available. Fallen who joini Aksor will be Shanks initially, but make it a point to eliminate them as well.
After Fallen; Servitor, Sniper Vandals and Stealth Vandals will also join the Aksor. Try to revive other players as this mission will fail if all the players die.
Here is a video on how to Complete Destiny Venus Winter's Run Strike Mission: