Unfortunately mounts are usually “one time” chances from gacha cubes. Sometimes they come back, so you will have to wait for each Goddess Cube and see if they release a pet in them. You can always shout, sometimes people have extras “eggs” (unused pets) they keep for selling, but prepare to spit up to 1 billion silver if that’s the case because those are damn rare.
Otherwise, if you don’t like the penguins you get as F2P, you can get the following pets without having to spend real money:
- Velheider (Companion Trader, 110k silver)
- Hoglan (Companion Trader, 453k silver)
- Lesser Panda (Mercenary Badge Shop)
- Guinea Pig (Guild Quest)
- White Guinea Pig (Medal of Honor Shop, 80 Boruta medals)
- Spotted Baby Pig (Adventure Journal Ranking)
Every other mount is from gacha. There were some other mounts available at one time from Adventure Journal Ranking (Baby Pig, Dodo, Armadillo), but those require coupons that are not available anymore, so unless you know people that have spare they don’t use and you can pool 20 of them, you won’t get those mounts (/me sighs at his 9 Armadillo coupons ).