There would be different answers to this, depending on what each person thinks is the easiest Moshling Set to get on Moshi Monsters.
The Ninjas are probably the easiest set to get since General Fuzuki is the only one which needs three specific color of seeds.
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The easiest moshling set to catch is the Dinos: Snookums, Pooky, Doris, Gurgle. Snookums is the easiest to catch because it needs and 3 Star Blossoms. You do not have to be a Moshi Member to catch any of the Dinos.
Boomer is a moshling that is orange and has a bandage on his head.Boomer the Bigmouth Squiddly Dee is part of the Noisies set on Moshi Monsters.
To get a moshling on the Super Moshi Missions you will have to complete the mission. At the end of the mission, you will be asked if you want to keep the moshling or not. If you click on "Keep It" the moshling will be added to your Moshling Zoo. If you click on "Set If Free", the moshling will be gone. Note: you have to be a paid Moshi Member to complete Super Moshi Missions.
It is unclear whether or not there actually is a moshling 001 as there is no spot for an 001 moshling in the Moshling Garden. However, Fuzzy the Furi is seen in the Moshi Magazine. Some think that Fuzzy is possibly part of a new set of Moshlings to come out in the future. Others think that Fuzzy was the very first moshling and is no longer a part of the Moshi Monsters game.
To catch Pip the Savvy Sapling on Moshi Monsters you have to purchase the "My Moshi Home" play set for the code to get the Nutty Flip seed. Plant the Nutty Flip seed with any two other seeds to attract Pip to your Moshling Garden.