While the ancient Romans were known to build "round ships" with a displacement of @ 500 tons (larger than the ships Columbus took to the New World), this is significantly smaller than a modern cruise ship. Even the Chinese "Treasure fleets" of the middle ages seem to have been @ 60m in length and displacing @ 2000 tons. While larger figures are sometimes quoted, the 60m length and 2000 ton displacement seems to be well within the capabilities of Medieval ship builders.
Speculative reconstruction of a Chinese Treasure Ship compared to a comparable European ship of the same period
While larger ships are more seaworthy, and capable of carrying more men and supplies, larger sizes may not necessarily translate into better performance against sea monsters. Indeed, should the monsters possess rudimentary intelligence, they may come to see larger ships as being better "prey" since more tasty humans are aboard.
Fending off attacks will depend on factors such as the speed, intelligence and composition of the sea monster. If it is a giant jellyfish, then simple avoidance manoeuvres may suffice, while if it is an intelligent Kraken, with the powerful musculature of a giant squid, then obviously much different tactics will be needed.
That "Oh Crap" moment when the Kraken surfaces....
For the most part, a large fleet will probably have smaller scout ships around the perimeter, to provide early warning or draw off the monsters. All ships will be equipped with harpoons, allowing the crew the ability to fight the monsters (even if it is largely symbolic, it is still good for morale). The upper decks of the ships might have nets or awnings suspended over them to prevent tentacles from reaching the deck, and trained crewmen with pikes or axes can attempt to pin the tentacles and strike them off (avoiding the stingers or other toxic parts as much as possible).
With Roman or Chinese technology, flinging burning barrels of oil into the water near where a Kraken is surfacing might force it to submerge again, breaking off the attack and allowing the fleet to change course or otherwise disperse and make a follow up attack more difficult. It the fleet has Byzantine technology, they have the ultimate weapon: "Greek Fire", a siphon and pump system to project burning fluid onto the enemy creature and the surface of the water, repelling the attack. Since Greek Fire was reputed to burn on water, this means the only defence for the creature is to submerge.
Roman "round ship". While it is not depicted carrying a catapult, you can see there is a large deck area to mount and operate one
Depiction of a Byzantine ship using it's "Greek Fire" projector
Finally, you can combine many of these features with special escort ships to protect the fleet, based on the armoured Korean "Turtle" ships. The crew can fight under protection of a spiked, armoured deck while projecting burning fluid and hurling harpoons and catapult darts at the attacking creature.
Replica of the Turtle Ship