It serves as the Boss of the Spire. A Leviathan monolith, it unfolds and reassembles into a geometric weapon of mass destruction, firing beams of burning Plasma energy. The only good thing about seeing it in such a mode, is that an apparent control core appears, from which the beam is emitted. This essentially is a Mexican Standoff-- and here you've brought hand weapons to a heavy artillery fight.
The Blaster Launcher will become available to you in the same mission as the Titan's appearance, and it holds a total of 9 rounds (and fires in 3-shot bursts, so you have 3 shots), so using it is extremely helpful in this fight. Scoring a hit on the Titan's core with the Blaster decimates it's HP. If you Lift an Engineer's turret, it may get in some shots as well. As it is a flying unit, ground-based weapons are, naturally, useless. There is a Supply Box in the room before, allowing you to change out weapons and packs: for Carter you may consider either a pack with Damage Reduction, or the pack that increases clip & carry capacity (the Blaster Launcher would then have a 4-shot clip, and 8 shots in reserve). Another good Agent makeup is two Scouts: the two guaranteed Critical Hits softens the target, and alternating with Decoy deployments may give Carter a reprieve from the devastating attack of the Titan.
For defense, always use heavy cover (which it will often destroy to get to you. If stuck in the open, your best bet is to run and dodge-roll to try to get it's targeting laser to lose tracking of Carter (or at least reduce time in the plasma field), as the Titan will almost always focus it's fire on him. The Recon's Decoy may buy you a few seconds, and Shields may at least reduce damage.
When the Titan does fire, the blast zone remains bathed in plasma, so don't linger if you do get hit.
Related salvage report
Salvage Report: Titan
Study of the limited sample of “Titan” material collected by intrepid XCOM agents shows many shared properties with the substance constituting Silacoids. Whether Titans or Silacoids are themselves sentient and can be regarded as living or are merely examples of highly advanced technology remains uncertain.
Titans are massive, airborne enemies, capable of shifting both shape and function. Field agents are strongly advised to find hardened cover when the Titan shifts into a distinctive “O-shaped” firing form, although this does expose what appears to be a vulnerable control core.