The asari, growing desperate as the Reapers attack their systems, have revealed an artifact that may hold the key to finding the Catalyst. Meet a scientific team at a temple on Thessia and investigate the artifact for clues.
Liara is a mandatory squad member in this mission. As such, the best things you can bring are Overload, Energy Drain and other anti-shield abilities which render Marauders vulnerable to Singularity and/or Warp. Another great priority is raw damage, which Liara simply doesn't provide a whole lot of.
Route to asari temple
In the first area, there's an Umbra Visor and supplies worth 4,500 credits towards the right, away from Lieutenant Kurin. Grab it before you do anything else, because speaking to Kurin will cut off access to the starting area. When the fighting begins, she directs you to use a turret gun to the right of the barrier. Multiple Brutes appear, as well as husks that will run towards the asari soldier's biotic barrier in an attempt to damage it. A Barrier Engine is located where the Brutes are spawning, and it will essentially double the enemies' ability to take damage until it is destroyed.
After a cutscene, proceed across the bridge. A group of Marauders and Cannibals flood towards you from the other side of the bridge. Take out the Marauders first. The far side of the area looks like a dead end, but the path is visually blocked by a wall. Continue forward to the end of the path and turn right. Proceed for more Marauders and Cannibals, as well as Spore Pods. After clearing the Marauders, go to the far left to pick up a M-560 Hydra missile launcher. As you move a little further up, Liara informs you of a door just ahead, but you need to deal with the Marauders and a Banshee first. Fortunately, the Banshee appears at a distance, giving you more time to damage it. The Hydra will be very helpful against them; however, the Hydra only contains one missile, so careful aiming is recommended. Before you leave the area, you can access two med-kits on the far right and far left of the area.
Walk along the path while salvaging the Terminal worth 7,500 credits, and subsequently bypass a door. A camera prompt will appear for a Reaper in the not-too-far distance. You'll also see three Cannibals crouching in the courtyard below; with the right abilities, you can kill them without firing a shot. Just to the right of the Cannibals is a broken shotgun that can be salvaged for 3,000 credits. Directly above the broken shotgun on a small ledge is a Med-kit and Shotgun High Caliber Barrel.
Make your way over to an asari sniper on the elevated area and snag the med-kit, Sniper Rifle Concentration Module and M-98 Widow before talking to her. Now take out as many enemies as you possibly can, including the Barrier Engine on the wall opposite you. The asari sniper will provide a constant stream of moral support, though her bullets may not be as effective. Once the coast is clear, proceed down the ramp to your left and collect ammo if necessary; there should be plenty. Go through the hole in the wall and to your left.
After the cutscene, you gain 450 experience and morality points depending on your conversation with the only asari soldier left at the outpost. Be careful of the Banshee as it can get ridiculously close within just a few seconds. Also take note of a Ravager just up the stairs, and a Barrier Engine on the far left, hidden by a partition. There is a M-560 Hydra missile launcher at your feet; for optimum use against the Banshee, retreat back to the way you came from and even further if necessary. Thankfully, you'll have some assistance from a gunship.
After you get rid of all the enemies, continue straight forward up the rubble and then to the right. Near the Spore Pods is an Assault Rifle Extended Barrel pickup. Past them, Husks attack you; past them, you tangle with two Harvesters accompanied by Marauders, Ravagers, and a Barrier Engine. Stick to cover, take shots at them whenever you can and watch out for any Swarmers. Consider falling back, which makes it easy to take out the Harvesters first, then get rid of the Marauders since they'll keep throwing up barriers and then get rid of the remaining enemies. Also be aware that you don't actually have to kill the Harvesters: once Talon Five is shot down, they will flee the battle. Continue forward and around to the left to find a SMG Heat Sink and a barrier for Liara to bypass, on the right of the temple entrance.
Temple of Athame
Make your way into the temple and pick up a med-kit close to the entrance. The scientists' bodies are lying on the ground near a large statue, which is the artifact you're looking for. However, before investigating the statue, search the temple for other artifacts to learn about the asari's history. If Javik is with you, he elaborates upon their history, better than Liara. When you investigate the statue, Shepard realizes that there is a Prothean Beacon in the temple. This helps explain how the asari are so advanced since they had the chance to study the temple for thousands of years and kept it a secret from the other species. You have to examine other artifacts to activate the beacon, which reveals a Prothean VI, Vendetta. When you're done conversing with it, it detects someone who is indoctrinated. Kai Leng delivers a hologram of the Illusive Man, who explains more about his goal to control the Reapers instead of destroying them. Regardless of what you say to him, you'll have to fight Leng.
Stay behind cover as he sends shockwaves that disable your shields. You'll need to move around a lot and use your squad to distract him to avoid a being struck from up-close. Once you take out about half of his shields a gunship will cover him while he recharges them. This will repeat several times. Just keep as much distance as possible and make sure to stay behind cover when the gunship starts shooting. When you get his barriers down, a cutscene will resolve the rest of the battle.
By the end of this mission, you will gain 15 Reputation, 15,000 credits and morality points depending on your conversation options.
EDI and Specialist Samantha Traynor tell Shepard that she tracked Kai Leng to the planet Horizon in the Iera system, making the mission Priority: Horizon available. The side mission N7: Communication Hub also becomes available.
Shepard will receive a message from Kai Leng, disguised as asari military command, gloating about defeating Shepard.
If Javik has been recruited you can witness a confrontation between him and Liara in the Port Cargo Bay on Deck 4 and have a conversation with Javik afterwards.
If Tali and Garrus are alive then Tali will be standing in front of the memorial wall on Deck 3 talking to Garrus over the radio and can be interacted with for a Reputation bonus (and again after talking to Liara for more Reputation).
Liara will be in her cabin and can be engaged in conversation.