The Cryo Beam (Tech) skill is required to get the "Icebreaker" achievement. Use the Cryo Beam skill to freeze an enemy, then jump and perform a melee attack. The enemy has to die from this attack to get the achievement. Set the difficulty to Normal or higher or else enemies will die before freezing. You will know they are frozen when they fall to the ground, unable to move. Stop using the Cryo Beam just before the enemy's health is depleted or else it will kill them.
The Flamethrower (Tech) skill is required to get the "Pyrotechnics Expert" achievement. Lighting three enemies on fire with one continuous flamethrower attack works best with enemy dropships. Wait under a dropship and when the enemies jump out, immediately use the flamethrower on them. You encounter a lot of dropships throughout the game. This can be done on the very first dropship in "Chapter 1: Planetfall" (Habitat 7). Every drop ship has at least a few enemies jumping off it at the same time. Make sure to set the difficulty to Normal or higher or else the enemies will die before they start to burn. You can also do this where enemies are standing close together so you can hit them all before the flamethrower runs out.
Go to "Hyperion - Habitation Deck" on the Nexus and interact with the Archive System. Select "General logs", "Asari archaeologist", and "Dr. Liara T'Soni" to listen to audio logs from Liara T'Soni. She is an asari researcher who appeared in all previous Mass Effect games.
In the Tempest ship, go down into the sleeping area next to the meeting room (Tempest - Deck 1) to find a Peashooter and Scientist toy on a bed.
Successfully complete the indicated task to unlock the corresponding achievement.
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