Since both these reagents cannot be harvested through the regular methods, you will have to farm for them, especially Amber.
For Turquoise;
Bought - Turquoise is occasionally available at the Bazaar. They are usually within limited amounts and more on the expensive side.
Fishing - If you fish, they can be found in fishing chests in the Nomad's Camp.
Mob Farming - A variety of mobs drop the reagent (not commonly though). Most bosses for example in Azteca drop the reagent. However common bosses which can drop both Amber and Turquoise includes the Gladiator in Mount Olympus and Cronus [Tartarus].
Amber
Amber like I said is a bit rarer, but uniquely has more opportunities of obtaining the reagent despite its scarity.
Bought - Brandon Mistborn sells an amber in exchange for 5000 arena tickets.
Fishing - Fishing chests found in the following castles/areas have chances of yielding the reagent:
Caliburn
Elephant Graveyard (also popular for code wands)
High Road
Outlaw's Refuge
Boabab Crown
Gardening - The following plants have a chance of dropping the reagent.
King Parsley (rarely)
Ultra King Parsely
Deadly Ninja Fig
Ultra Helephant Ears
Ultra Huckleberries
Ultra Trumpet Vines
Red Huckleberries (Very rarely)
Red Bell Pepper
Ultra Tiger Lily.
Mobs - Again, the gladiator seems to be a little more lenient with dropping this reagent as opposed to other mobs. Give him a few runs. All bosses within the Tatarus dungeon also drop the reagent.
