Burning Down the Hive
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This mission is part of the Level 1 epic arc, called The Blood-Stained Stars, otherwise known as the "Sisters of EVE epic arc". This 50-mission arc is highly recommended for any new player of EVE Online. However, it has a few missions that can be difficult - and "Burining Down the Hive" is one of these. Rare is the new player who does not suffer his or her first ship loss in this mission.
How Do I Get This Mission?
Burning Down the Hive is a mission in the Level 1 epic mission arc for the Sisters of Eve faction. The arc begins with agent Sister Alitura in the Arnon system. Career tutorial agents provide a link to Sister Alitura when you complete their arcs. See this link for a complete mission-by-mission guide: The Blood-Stained Stars
What Makes This Mission Special?
The first room of this mission features multiple Strain Infester Alvi or Strain Render Alvi rogue drones that webify and warp scramble your ship. If the rats get within range and scram you, then you will not be able to warp out of the mission deadspace to preserve your ship. This is the only Level 1 mission that has warp scrambling rats; you will not see them again until Level 3 missions.
How Do I Survive?
You must do two things to survive: Fit your ship properly, and use the correct tactics. In missions up to this one most players will have been taking the approach of diving in to the enemy group and fighting them at short range, warping out if you bite off more than you can handle. In this mission the presence of warp scramblers and the large number of enemy ships makes this unlikely to work. The key tactic to this mission is one called "kiting", where you fit long range weapons and keep the enemy at range so that they can't damage you much, and to avoid being caught by warp scramblers and webs.
Fitting
The key here is to be fast, and to destroy the warp scrambling drones from outside their range (approximately 10 km). An afterburner is essential as these drones have a speed of 900 m/s. You should use long range weapons, aiming for a range of 15km. Tracking is not an issue. As usual for rogue drones, EM and/or Thermal damage is preferable. If your ship has a drone bay then this will help a lot, since your drones can damage enemies up to 25 km with no problems.
A Punisher with pulse lasers and long-range crystals (microwave or radio) has been effective in this mission, but for other races, fit light missiles, railguns, or artillery to get the range you need. A Destroyer with its range bonus and increased DPS (but reduced speed) may work better than a frigate. With the addition of drone destroyers, such as the Algos and the Dragoon, you can easily take down the entire mission with light drones at range. The choice is yours.
Tactics
When you first warp to the mission location, there will be a few rogue drones and an acceleration gate. Destroy the drones; this first group has none of the scrambling drones. Once you are done, activate the acceleration gate.
Once your warp is done, sit and watch the rats move for a short time. You will receive a message that your drone - cruiser size and called the Mysterious Drone - has left through an acceleration gate. You will see that there are two groups of rogue drones, 14 in total, which merge and then separate. You will want to engage the two groups separately, unless you feel lucky. Once you see two distinct groups, lock one Strain Infester/Render Alvi drone and fire at it; you will likely miss since you are out of range, but the first group (and only the first group) of rats should still start chasing you.
Once the drones are chasing you, turn your camera 180 degrees in the opposite direction from them (so that they are 'behind' you) and double-click in space to move away from them. This is a tactic known as "kiting", where you move steadily away from your enemy while matching speed with them, keeping them at your optimal range. Keep an eye on your overview, and start shooting drones when they enter your range. If they're not catching up, slow down your ship; if they're gaining too fast, activate your afterburner. Make sure that none of the Strain Infester/Render Alvi drones get closer than 10km to you. The drones have short range weapons and will do very little damage at over 10km, while your weapons should be able to damage them consistently. Continue until all drones in the first group are destroyed, then repeat the process for the second group.
Fly back to the next acceleration gate and finish the mission; the drones in the last room pose no significant challenge.