I'm not sure if some of these are posted in the site i will post useful tips that i've searched around online. I will post the stuff i find most useful. Post a response if this helped. Not sure if im suppose to post any links on this website or not, but err if you want the website where i found these info then post here. I will pm you the link if im allowed to.
Speed: Every fifth minute of the hour (example: 5:05)
Defense: Every tenth minute of the hour (example: 5:10)
Strength: Every thirty minutes of the hour (example: 5:30)
Life (Hit Points) : Every hour of the day (example: 5:00)
Level: Every two hours of the day! (example: 3:00, 5:00, 7:00 NST)
Doubloons: Every 55 seconds past the hour
Burnt Food: 11:00 - 12:00 NST
6:00-7:00 am NST
2:00-3:00 pm NST
10:00- 11:00 pm NST
The Wheel of Excitement - If you play the wheel of Excitement exactly on the hour (NST), 90% of the time you win 10,000 np! (not sure if this is true...)
Krawk Pirate Avatar: Visit Room 2 at the academy.
Aisha Pirate Avatar: Visit Room 45 at the academy.
Shoyru Pirate Avatar: Visit Room 15 at the academy.
Scorchio Pirate Avatar: Visit Room 2149 at the academy.
Edna Cackle Avatar: Randomly given out as prizes in Edna's Witch Quests when you complete a few quests.
Queen Fyora Avatar: Purchase an item from the Hidden Tower.
Wheel of Excitement Avatar: Win 10,000 Neopoints on the Wheel of Excitement.
Adam Avatar: Have the same amount of Neopoints as Adam.
Werelupe Avatar: Own a Werelupe and go to its pet lookup.
Free Jhuidah: A Tabogo Potion was to be brought to Jhuidah, who at the time was trapped in a fish bowl. This avatar can no longer be obtained. (Retired)
Meridell Knight Avatar: If you participated in the Meridell side of the Meridell war, visit your userlookup.
Darigan Darkling Avatar: If you participated in the Darigan side of the Meridell war, visit your userlookup.
Saved Mystery Island Avatar: You had to have been one of the first 10,000 people to solve the Island Volcano Mystery.This avatar can no longer be obtained. (Retired)
Volcano Rewards Avatar: You must have been within the first 75 to solve the mystery plot. This avatar can no longer be obtained. (Retired)
TCG Wizard Avatar: Given out to TCG Tournament winners.This avatar can no longer be obtained. (Retired)
Dr. Sloth Avatar: Random Event.
Grey Faerie Fallen Avatar: Visit Grey Faerie's Neopedia article.
Anglepuss Angel Avatar: Visit an Angelpuss item lookup.
Soup Faerie Kind Avatar: Feed your pets until they are full, at the Soup Kitchen.
Faerie Grundo Avatar: Visit a Faerie Grundo's lookup.
Maraquan Krawk Avatar: Visit a Maraquan Krawk's lookup.
Usukicon Shop Keeper Avatar: Watch the Usukiland Advertisement.
Usukicon Usuls Avatar: Watch the Usukiland Advertisement.
Techo Master Avatar: Visit the Training School of Wisdom in the Island Trading School.
Dr. Death Avatar: Visit the page to Abandon Your Pet.
Defenders of Neopia Aisha Avatar: Go to the Defenders of Neopia game.
Defenders of Neopia Lupe Avatar: Go to this Page in the Defenders of Neopia.
Plushie Eyrie Squawk Avatar: Go to the Neopets Chat Boards and reply to a message typing Squawk.
Math's Nightmare Avatar: Get a score on the top 200 in Math's Nightmare.
Jhudora's Cloud Avatar: Complete level 20 or higher in Jhuadora's Cloud.
Illusen's Glade Avatar: Complete level 20 or higher in Illusen's Glade.
Better Than You Avatar: Complete a Better Than You competition.
Capara Avatar: Beat Capara in the first round of Cheat after fully completing the Cheat Tournament.
Grundo Snow Throw Avatar: Receive a high score playing Grundo Snowthrow.
Escape From Meridell Castle Avatar: Win a trophy from Escape from Meridell Castle.
Freaked Korbat Avatar: Get in the top 50 or 100 of the high score list in Korbat's Lab (unconfirmed).
Avatar Collector Avatar: Be on the top 50 collectors of avatars.
Chocolate Avatar: Buy an item from the Chocolate Factory Shop that has a rarity of 90 or higher.
Evil Poogle Plushie Avatar: Have a Malevolent Sentient Poogle Plushie (TCG) Item in your inventory and refresh your inventory
Meowclops Avatar: Add a Meowclops as a petpet for your active pet.
Anglepuss Avatar: Equip an Anglepuss to your neopet and refresh the pet reference page.
Codestones Avatar: Have all 10 codestones in your inventory.
Mad About Orange Avatar: Hold over 8 items with the word "Orange" in their name, in your inventory.
Pant Devil Taunt Avatar: Buy an item worth one million Neopoints from the Hidden Tower and then put it in trades. Refresh the page repeatively.
Feed Me, Hungry Skeith Avatar: Feed any item with the word 'Skeith' in to a Skeith.
Coconut JubJub Avatar: Feed a Coconut Jubjub an item with the word coconut in it.
Chokato Avatar: Have the Chokato (TCG) item in your inventory and refresh multiple times.
I'm Smelly Avatar: Have 10 different dung items in your inventory and refresh multiple times.
Jetsam Chomp Avatar: Feed a Jetsam a Pepito.
Fuzzle Boo Avatar: Buy a Blue Evil Fuzzle and play it with your pet. When at the play window, refresh over and over until you receive the avatar.
Space Faerie Avatar: Defeat the space faerie in the battledome.
Heermeedjet Avatar: Defeat Defenders of Neopia Round 8. To find the Meerca Brothers, click here and refresh a few times.
Meerouladen Avatar: Defeat Defenders of Neopia Round 8. To find the Meerca Brothers, click here and refresh a few times.
Grarrl Warrior: Equip one of the new Grarrl weapons that were realeased on Grarrl day.
Extreme Potato Counter: Receive a trophy on the game Extreme Potato Counter.
Deadly Dice Avatar: Win at Count Von Roo's Deadly Dice game.
Mystery Island Stamp Avatar: Complete the Mystery Island page of Stamp Album.
Virtupets Stamp Avatar: Complete the Virtupets page of Stamp Album.
Tyrannian Stamp Avatar: Complete the Tyrannian page of Stamp Album.
Haunted Woods Stamp Avatar: Complete the Haunted Woods page of Stamp Album.
Plushie Tycoon Avatar: Receive a trophy in Plushie Tycoon.
Black Pteri Avatar: Defeat him in the Battledome.
Zurroball Avatar: Receive a trophy in Zurroball.
Coltzan Avatar: Have him raise the HP of your Neopet. (Retired)
Harris Sleep Avatar: Equip between 24:00:00 pm and 1:00:00 am NST.(Retired)
Wand of Dark Faerie Avatar: Equip a Wand of the Dark Faerie to your neopet. (Retired)
Brain Tree Bad Day Avatar: Complete the Defenders of Neopia mission 5. (Retired)
Rainbow Faerie Avatar: Complete the Rainbow Faerie Quest. (Retired)
Kadoatie Sulk Avatar: Equip a Kaodotie petpet to your Neopet and refresh the pet reference page a few times. (Retired)
NeoPets Version 2 Avatar: Unknown