The Andromedon is an alien unit inside a "Battlesuit", which it seems to require to shield it from Earth's atmosphere. It is an extremely heavy enemy, appearing in the endgame armed to the teeth.
It is equipped with a plasma rifle, dealing 9-11 damage and shredding 2 armor. It can also launch an acid bomb, which deals 5-7 damage and shreds 3 armor in addition to causing Acid Burn for additional damage over time.
It can destroy cover by walking through it and has a melee attack similar to the Faceless, in that it destroys cover around the target. While powerful, the melee attack has low accuracy.
The Andromedon is extremely durable, with 12-21 HP (depending on difficulty) and 4 armor (3 on Rookie). The Battlesuit means that it is immune to fire, poison and acid, although Acid Grenades and Bombs will still shred its armor.
Upon "killing" the Andromedon (smashing the cockpit to kill the pilot), the Battlesuit's AI will activate an autopilot function, trailing acidic coolant all over the ground as it moves and attacking nearby XCOM soldiers. Fortunately, the Andromedon Shell is disarmed and can only attack with its fists. It also loses its armor pips and immunities.
The Andromedon is interesting in that the piloted and autonomous suits are two different units. The piloted suit is organic, so Psionic attacks such as Insanity and Domination are effective. The Andromedon Shell counts as a robotic unit, so anti-robot attacks such as Haywire Protocol, Bluescreen Rounds and EMP Grenades/Bombs will be effective.
Mind control of an Andromedon ends when it is killed and turns into a Shell - it will no longer be on XCOM's side after the Battlesuit AI activates. This means that if a mind controlled Andromedon is killed, even under Domination, the Shell will return and act on the next alien turn.