Upon leaving the Communications Tower you'll discover your party is being pursued by a big spiderbot, intent on obliterating you. This is a very important part of the SeeD exam as there are dozens of variations in how you can handle this particular bot, and which one you choose can have a profound impact on your ending exam score. Your three options here are: Evade, Run Away, and Destroy. Depending on how you've played the game up til this point the Destroy option may or may not be on the table.
Evade: Evading the boss means avoiding any confrontation with it. This is incredibly challenging to do, and requires you be very meticulous in your actions. Evading the boss will give you the highest SeeD score, but you will lose out on massive amounts of AP. To evade, first you must defeat it in the initial battle. The boss will shut down, during which time you'll be prompted to run away. Do so. From here on out you have to avoid getting back into battle with the boss (which repairs itself) to get the highest score. At the first screen, run quickly away. At "Selphie's Cliff" run directly left, avoiding getting caught on any rocks. On the next screen, you have to press your Walk button, or else the leaping spider will daze you and catch up. On the bridge, wait for it to leap over you then run back to the left. When it leaps again quickly switch to running right and away. From here on out, avoiding it is easy. Make sure you use your action button near the dog in the square to rescue it for more points. When you encounter squad C coming out of the building on the right, don't go through the door they came from - It will deduct massive points. Keep running away until the cut scene / animation takes over.

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Run Away: Running away is the easiest way of dealing with X-ATM092. You'll get tons of AP for your GFs, but will not get the highest possible SeeD score. With the Running method, you simply battle the boss every time it catches up to you. Attack it until it shuts down, then run away. You still want to rescue the dog in the square, and do not want do go through the door squad C comes from. What's nice about this method is you can redeem some of your lost points by taking your sweet time with it - which also allows you to draw lots of the boss' Protect magic. Protect is a positive status effect which will negate large amounts of physical damage when cast on your party. Additionally, the closer you come to using the full 30 minutes, the higher your score will be.
Destroy: As I mentioned before, destroying the boss is only an option if you're prepared for it in advance. Destroying the boss is required for what people term a "perfect game", but this guide is not intended for that purpose. To destroy it, you would have to have grinded and farmed extensively before even setting out on the exam, getting very high level magic and junctioning it to Squall. After that, you would have to force him into his Limit Break to even have a chance at destroying the boss. Just playing the game through normally, you'll never be able to do enough damage to the boss to destroy it before it repairs.