Some bestiaries and chests can be missed in some areas/dungeons, you won't be able to go back once you missed one of them so make sure to use you saves properly. Below is a list of missable areas/dungeons in order of game progression:

Castle Hein is the first dungeon that you will be able to go back once you defeated Hein. Here the list of monsters and items:

Chests (14):

• Phoenix Down (x4)
• Holy Arrow
• 3000 gil (x3)
• Bomb Fragment
• Antarctic Wind
• Zeus's Wrath
• Royal Sword
• Elixir
• Rune Bow

Hidden Items

• Mini

Monsters:

• 066. Pharaoh
• 067. Lemur
• 068. Lamia
• 069. Demon
• 070. Dullahan

Wracked Ship disappeared after defeated Kraken inside Cave of Tides. There are no monsters here, but 2 chests you need to collect:

Chests (2):

• Blood Sword (missable)
• Zeus's Wrath (missable)

Sea Surface divided by 3 areas by monster group. Floating Continent Inner Sea, Floating Continent Outer Sea, and Surface Word's Sea. You will lose access to sea surface after the Enterprise is destroyed when you fly over Saronia.

Monsters:

• Floating Continent - Inner Sea
  • 031. Killer Fish
  • 032. Hermit
  • 033. Sea Elemental
  • 034. Tangie
  • 035. Sahagin
• Floating Continent - Outer Sea
  • 071. Anet
  • 072. Mermaid
  • 073. Seahorse
  • 074. Sea Serpent
• Surface World - Sea
  • 112. Sea Dragon

Gungnir is the best lance in the game with an attack power of 140. In order to obtain this rare weapon, you must steal it from Odin (Saronia Catacombs).

Item:

• Gungnir

Lake Dohr located on Floating Continent, but you can only access it way later in the game. The cave has 19 chests and 4 monster types:

Chests (19):

• Phoenix Down
• Heavenly Wrath
• Earthen Drums
• Arctic Wind
• Hi-Potion (x3)
• Elixir
• White Musk
• Aegis Shield
• Platinum Hammer (x2)
• Bacchus's Cider
• Turtle Shell
• Black Hole
• Reflect Mail
• Black Musk
• Lilith's Kiss
• Raven's Yawn

Monsters:

• 139. Ouroboros
• 140. Plancti (missable)
• 141. Sea Lion (missable)
• 142. Remora (missable)

This dungeon is a also one-time visit so make sure that you collect all chests and bestiary list and chests.

Chests (8):

• 10000 gil (x2)
• Rising Sun
• Lust Dagger
• White Musk
• Chocobo's Wrath
• Phoenix Down (x2)

Monsters:

• 155. Peryton
• 156. Ogre (missable)
• 157. Cyclops (missable)
• 158. Nemesis (missable)
• 159. Humbaba (missable)