On the bright side, it doesn’t have to be the 5k that others are suggesting.
Assuming absolute 0 luck, from Tier 3 to Tier 6, you can spend 1000 Gems for 10 Lil’ Freedoms. You get at least 1 from the Pet Rescue and 1 from a 3rd day login bonus for the July 4th thing if you’re still on track for that.
You need a total of 31 pets to reach Mythic.
So after Tier 1-6 (for 1,075 gems), you’d have to spend a max of 2,000 more gems: 20 * Tier 7 (100 gems) to get to 31 copies. 1900 with tomorrow’s login bonus. Hopefully your luck isn’t absolutely horrible and you can get extra pets from the baskets while purchasing Tiers which will cut the cost down more.
Now if you have to buy the food too, it’ll hurt.