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Feed your pet any item with the word 'Custard' in it's name.

Tip: A cheap custard item is 'Green Tea Custard'.
On Portugese you can feed your pet any item with the word 'Cream' in it's name.

Visit a Purple Peophin's lookup.

Taesi

Qisal

cheerios_22

Have any kind of submission published in a 50th issue of the Neopian Times, (ie. 200, 250, 300, ... etc.). As of 2023 (Y25), it has been changed to every 25th issue of the Neopian Times.

Visit a Camo pet's lookup.

Gyrrant

Kasandaria

Pawrah

Have the petpet Mummy Baby attached to a Halloween Ruki for 30 days, and then view its pet lookup.

Win at least 4 rounds in a row at Kiss The Mortog and then collect your winnings.

Have your petpet turned to soot by the Petpet Labray.

You can only get access to the Petpet Lab if you have access to the regular pet lab. This means you need to complete both the 9 pieces of Secret Laboratory Map, and the 9 pieces of Petpet Laboratory Map.

Tip: Visit SunnyNeo.com's Petpet Laboratory page for more information on the Petpet Lab Ray.

Own a fire blumaroo that has a fire petpet attached to it for a minumum of 30 days.

Visit the lookup of a pet with a Scarabug as petpet.

Fenris_Lobo_Alado_

Kithyia

Mikimoy

Visit the lookup of a Halloween Meerca.

Meerca

SeaMeecra

Taellia

Score 3,600 or more points at Typing Terror.

Score 1,100 or more points at Grand Theft Ummagine.

For some help you can take a look at Hawk_y2K1's Petspage

Score 1,500 or more points at Volcano Run 2.

Tip: Visit SunnyNeo.com's Volcano Run II guide.

Visit the lookup of a pet with a Spardel as petpet.

abbywabbywoohoo

buster25212

Karmatica

Visit the Draik Nest while you have a Draik as your active pet.