By finishing side quests, you get a little more time added on until the end of the world. The Main Quests offer 1 extra day each while side quests add on a little bit depending on difficulty. The formula is quite complex so all you need to know is that you need to finish around 40 side quests to gain the Extra Day. This is entirely possible during the course of a normal playthrough and you get plenty of time to finish all side quests if you use the time correctly.
Complete the God’s Trials on the Final Day inside Luxerion Cathedral. Doing so rewards you with the Ultima Weapon and Shield. See the Final Day section of the walkthrough for more info.
Defeat Aeronite in the Dead Dunes from Day 7 onwards. See the side quest “What Rough Beast Slouches” for tactics and a video. Aeronite is the strongest monster in the game and requires an advanced knowledge of the game mechanics and a good setup. It is best attempted during the final days of the game around Day 12 or during the Extra Day.
Deal 100,000 damage or more in a single blow. This can be accomplished fairly early in the game during the battle with Noel. Equip the Dragon’s Blood garb and the Thunderbird Bracelet. Take in debuffs like Deprotect and Deshell then Stagger him. During the Stagger, if you keep hitting him with attacks he’s vulnerable to, you will get the option to Launch him. Do this and then use the Smite option (what was Heavy Slash) immediately and that should do well over 100,000. See the Noel Boss Fight video in the section 1-5.
From Day 9, some Canvas quests will appear asking you to re-open the old highways between each place. This is simply a matter of either unlocking doors, collecting items and whatnot. Look in the Canvas section and main walkthrough for more information.
Exterminate all the enemies of a species, and the Ω, or Last One, will appear. This is a significantly strengthened version of the species and will take a strong Lightning to beat some of them. You probably won’t encounter any Last Ones until at least half way through the story (Day 6 onwards). See the section “Ultimate Lair and Last Ones” in the guide for info on how to beat them.
Kill your first Last One enemy. This will likely be one of the frequently encountered enemies like Goblots or Niblets. Check the Ultimate Lair section of the walkthrough for more information on killing them.
This garb, the Ultimatus garb, is obtained from beating the Ultimate Lair during the Extra Day. You must complete all 33 floors and kill the final boss Ereshkigal to receive your rewards. See the Extra Day section of the walkthrough.
Kill 30 little green lizards in Dead Dunes. You can find a ton of these around the Oasis Lighthouse area and many more scattered around the Dunes. During your frequent visits there, make sure you kill any lizards you see.
Conquer the Ultimate Lair and take down Ereshkigal for this trophy. See the relevant section of the walkthrough.
Win 10 battles at the Slaughterhouse in Yusnaan. The Slaughterhouse is only open at night and the enemies vary depending on the time. This is easy to do and you can get some decent prizes for winning.
Collect Soul Seeds that appear from Chaos Infusions. These glowing purple egg-shaped things can be sold to a Soul Seed Trader for a decent sum of money and are worth collecting whenever you find them. You can make daring forays into Infusions even if you have no intention of fighting the monsters. Beware that beasts are much more powerful inside Infusions!
Restore the Angel of Valhalla to full health. See the walkthrough Chapter 3 in the Wildlands for information how to go about this.
You will gain this trophy when you have obtained an Elixir. There are two ways of doing this: Collect 100 Soul Seeds and hand them over the a Trader and in return, you will receive the Elixir as a reward. The other way requires a hefty 360,000 Gil but you can then purchase one from the Outerworld Service via an NPC player. People usually leave messages stating they have an Elixir so have a look at each NPC you come across if you have the cash.