Advanced military career (mission arc)
This is the advanced military career mission arc available from advanced military career mission agents. Missions in this chain do not invoke tutorials that give items. Missions described are presumed to be universal, though only the Gallente version is documented here.
Blow up some frigates: 1 frigate alone, then 2 frigates after that, then 3 frigates after that. Total of 6 frigates to be destroyed. Easy. Reward: Propulsion Jamming skillbook.
Angel of Mercy
The agent will provide a frigate. (For the Gallente, it's an Atron.) Assemble it, make it active, strip it (it shouldn't have modules to begin with, but make sure), undock, take it to the mission site, and collide with the pirate base. There are three enemy frigates, but as long as the approach is started immediately, they won't hit you. The base is a Large Collidable Object or Structure. Your frigate will explode, leaving your pod. All enemy frigates will be destroyed in the same explosion.
Only Tech 1 frigates are admitted into the mission space, probably because the destruction of the player's ship is scripted.
Your Undivided Attention
The agent provides a Civilian Warp Disruptor. There are no acceleration gates; you are dropped 20 km from the "Fleeing Pirate". Warp Disrupt the primary target. DO NOT DESTROY THE PRIMARY TARGET. Secondary targets despawn once the Fleeing Pirate is warp disrupted. Warp back to your agent.
A Friend in Need
The agent provides a Civilian Remote Armor Repair System. No acceleration gates. You're dropped about 9 km off of an NPC called "Damaged Vessel". Use a remote armor repair on it and the mission will complete. Reward: Remote Armor Repair Systems skillbook.
The acceleration gate admits only Tech 1 Frigates and Rookie Ships. The agent provides a frigate with no fittings (for the Gallente, it's an Atron). You are required to destroy at least one enemy ship and then continue fighting until your own ship is destroyed. The agent explicitly warns you in red text not to use an expensive ship.
Upon jumping the gate, there is a single enemy frigate. Destroying it causes 3 Spider Drone II and about a dozen cruisers to spawn; these vessels will use webifiers and EWAR (for Gallente, this is sensor dampening). On the Gallente version, there's really nothing you can do to fight back, since you're dampened so much that you can't lock anything. So, just have the local station selected and warp your pod out when your ship is destroyed.
Don't Look Back
The agent provides a Civilian Afterburner. There is one acceleration gate, normal restrictions. Upon warping to the initial gate, you get a transmission, which accurately describes the situation. Jumping the gate drops you 27 km off the Asteroid Station, a Large Collidable Object. You take (what I presume is) 50 EM damage every 6 seconds until you get to the Asteroid Station. Once you get another transmission from your agent, warp back to your agent.
Caldari Reward: A copy of the Light Missiles skillbook.
Weapon of Choice
For the Gallente: the agent provides 2 Civilian Hobgoblins. There are no acceleration gates; the warp-in point is 9 km from your target. You must use a drone or drones to destroy the target.
For the Caldari: the agent provides a Civilian Gatling Railgun. There are no acceleration gates; the warp-in point is 9 km from your target. You must use the Civilian Gatling Railgun to destroy the target.
The acceleration gate has normal restrictions. The mission talks about fleets and fleet commanders, though you won't actually be in a real fleet as far as the game engine is concerned. Starting at initial warp-in, an NPC CONCORD "Fleet Commander" will give you orders by pop-ups that appear in the middle of your screen. Read the first one carefully before you jump the acceleration gate. NEVER OPEN FIRE ON ANYTHING OR ANYONE.
What you're expected to do is jump the gate, then hold position until you get the CONCORD pop-up ordering you rescue the hostages. Once you get that order, fly to the Prison Facility as though it were a cargo container; get within 2500 meters, open it up, and move the hostages to your cargohold. Then warp out of the immediate vicinity and bring the hostages back to your agent.
Reward: 17000 credits and 21000 bonus credits.
The agent will provide a Civilian Stasis Webifier. There is no acceleration gate; warp to the mission location. You will land 32 km from a Pirate Leader, get within webifier range, and webify the target, but DO NOT SHOOT HIM. Close the pop-up from the Pirate Leader and maintain the web until you get a pop-up from CONCORD saying that they'll take it from there. The Pirate Leader's ship will turn into a wreck due to a scripted event. Warp back to your agent.
Reward: One copy of the Destroyers skillbook.
The agent provides a Tech 1 Destroyer (of the same race as the agent). There are no acceleration gates. No hostiles are immediately visible upon warpin, though a pop-up appears informing you that the hostiles are getting into their ships. The Terrorist Leader and two Mercenary Trainees spawn about 25 km away; they are all frigates. You are required to destroy the leader; you may destroy the wingmen at your discretion, but this is not required unless they're the ones warp scrambling you (see below).
The mission description and the tutorial it triggered warned of enemy webification and warp disruption on you. I used a catalyst with 4 railguns and four blasters. I killed the leader from a constant distance of 20 km while kiting him using lead charges in the railguns, and then closed to within 5 km of the trainees and killed them using my webifier and antimatter charges in the railguns and blasters. I did not notice enemy webification or warp scrambling/disruption; it's possible these were being mounted by the leader, who never got in range to use them.