Lloyd has a grand total of 29 titles available. This solution contains SPOILERS for the main quest and several side quests.
Here they all are, in the order they are shown in the menu:
Swordsman: This is Lloyd's default title.
Drifting Swordsman: You will gain this automatically during story progression.
Eternal Swordsman: You will gain this automatically during story progression.
Gourmet King: Lloyd must fully master all 24 recipes.
Nobleman: Lloyd gets this automatically during the dinner party event late in the game. In order to access this event, you must have already seen the Flanoir doctor scenes, and saved Princess Hilda from her kidnapping, which only happens after completing the story events at Latheon Gorge.
Arrgh, Me Hearties: Early in the game, in the town of Izoold, Lloyd agrees to deliver a letter for a girl named Layla. After witnessing the Flanoir doctor scenes and rebuilding Luin, visit the docks to find the letter's recipient, Aifread. Agree to buy the boat, then leave Luin and re-enter. Speak with Aifread again to gain this Title.
Beach Boy: Lloyd gets this automatically during the beach costume event. After witnessing the Flanoir doctor scenes, visit Altamira and speak to the woman in front of the hotel. Find her daughters and you will gain a scene at the beach.
Unrivaled Blade: Lloyd must choose to talk with Kratos during the Flanoir doctor scenes. This requires Kratos to be in the party instead of Zelos, and also that he is in the top three for affection. After these scenes, you must then progress far enough to unlock Sheena's duel. After that sequence is done, immediately talk to Taiga in Mizuho to unlock this Title.
Gentle Idealist: This is obtained during the story events in the village of Mizuho.
Peeping Tom: This is only available if you have Zelos in the party instead of Kratos. After viewing the Flanoir doctor scenes, visit the hot springs. The male party members will use the facilities first, followed by the women. During the second visit, Lloyd will gain this Title.
Midlife Crisis: After clearing the story events at the Remote Island Human Ranch, return to Triet. There is a man standing near the Inn who will host a minigame for Lloyd. Get a combined score of 100 to unlock this Title.
Palmacosta Pro: While in the city of Palmacosta, after completing the events at the Palmacosta Ranch, you can speak with a guard standing outside in the same area as the Governor's Office and the church. Lloyd will participate in the Orienteering mini-game, and if you succeed, you will unlock this title.
Sword of Swords: This Title unlocks after Lloyd completes the Advanced Coliseum battles. The Coliseum can only be entered when there are 8 people in the party.
Tactical Leader: This Title unlocks after you complete the Advanced Team Coliseum battles with Lloyd in the party. The Coliseum can only be entered when there are 8 people in the party.
Grand Swordsman: This is unlocked by reaching level 20.
Master Swordsman: This is unlocked by reaching level 40.
Holy Sword: This is unlocked by reaching level 100.
Combo Newbie: Get at least a 10 hit combo in any battle. This gets easier the further into the game you get, but I unlocked this during the fight with Vidarr, the first boss of the game, at Martel Temple.
Comboist: Get at least a 30 hit combo in any battle.
Combo Expert: Get at least a 60 hit combo in any battle.
Combo Master: Get at least a 100 hit combo in any battle.
Tetra Slash: In battle, you need to do a three hit combo with directional attacks. These are different attack animations that happen while you hold the stick while pressing X to attack. You need to do three different attack types (Up, Down, Side, or Neutral) and then follow it up with a Demon Fang. You'll get a prompt at the end of battle if you've done it right.
Brave Soul: Do not run from any battles until you fight Yuan and Botta in the Tethe'alla Base.
Lone General: In any battle, have the other three characters die. This is easiest by setting them to Manual control, then letting enemies kill them. Hold down L1 and use any directional button on the D-pad to have Lloyd issue an order. You need to wait and listen to his entire voice line. Do this a total of 10 times, then finish the battle.
Boorish General: Go into Lloyd's Tech commands and assign Techs from other characters to the L2 and R2 buttons. While in any battle, activate those abilities a total of 10 times in a single battle.
Gung-ho: Enter the fight with Rodyle at the Remote Island Human Ranch with a battle party average level of less than 145. That is an average character level of 36. This is best attempted on New Game +.
Eternal Apprentice: Do not remove the Wooden Swords weapon from Lloyd until after the fight against Kilia in Palmacosta.
Berserker: In the main menu change the difficulty to Hard. You need to complete 256 battles on Hard difficulty to unlock this title. I recommend returning to the area around Iselia to speed this up with weak enemies.
Guardian: If you have a save file from Tales of the Abyss, this will unlock for Lloyd when you start the game. Otherwise, it does not unlock until you start New Game +.