The last thing you must do to beat "Monster Hunter Tri" is repel a Ceadeus to save Moga Village. Once you do this, a post-game quest called "The Decisive Battle" becomes available, which is essentially a repeat of the final quest with one major change: You are now able to kill the Ceadeus. Even if you managed to repel the elder dragon Caedeus in the first quest with no problem, killing him proves to be a significantly harder feat.
Prepare for the battle. Speak with Cha-Cha before the battle and have him equip the Ancient Mask -- this allows him to replenish your oxygen during the battle. Equip your hunter with a weapon with a fairly long range to it, preferably a lance or longsword imbued with either fire or lightning. Stock up on Mega Potions, Whetstones, Waterblock berries and Dragonfell berries.
Save your game and start the battle. The arena is composed of three different areas and you must swim after the Ceadeus while attacking it as much as possible. You also have a 35-minute time limit.
Attack the Ceadeus' weak point -- its large mane near the bottom of its face. Keep slashing at this point to whittle away at its Hit Points (HP) until you get to Area 3. If you need Ceadeus parts, like its tail or horn, attack these areas until they break. Unlike some creatures, the Ceadeus' tail will not fall off once broken -- it will appear that chunks of flesh have been ripped away once it is broken. One of the Ceadeus' horns will fall off to indicate that it is broken.
Dodge the Ceadeus' attacks. It does not attack very frequently but, when it does, it hits very hard for a lot of damage. Move below it if you see it drawing in water to avoid its cyclone attack. If it starts to swing back, move behind it to avoid its powerful swipe. Move out of the way if you see the Ceadeus start to wiggle back and forth -- this means it is about to charge forward. Resume your attacks as soon as the Ceadeus finishes attacking.
Replenish your health and cure any status effects using the items you stocked up on earlier. Have Cha-Cha replenish your oxygen as necessary by pressing "Select," then pressing "Start." Use Whetstones to sharpen your weapon.
Mount your final attack in Area 3. Swim over to the Dragonator, which is in the left part of the area. Use the onscreen instructions for operating the ancient weapon and aim it at the Ceadeus' mane. Fire the spikes at its face and move away from the weapon. Pay attention to your screen because you are notified when the weapon is ready to use again.
Swim to either of the Ballistas, which are visible from the Dragonator, and use them while the Dragonator charges. Before getting onto the Ballista, gather ammunition from the broken crates near each one, then select the ammunition in your inventory as if you were going to use it like a health item. Follow the onscreen instructions for using the Ballista and shoot the Ceadeus in the face. If you haven't snapped off its horns yet, the Ballista is a good weapon to use to finish them off.
Use the Dragonator again once you are notified that it is ready to use. Continue alternating between the Dragonator and Ballistas until the Ceadeus is dead.
Don't worry if you don't kill the Ceadeus on your first try due to the time limit -- Caedeus does not regenerate his health in subsequent attempts.