Difficulty: Medium
A lot of these will unlock their own trophies and have their own guides to unlock.
You can check which you already have in-game via the options menu.
Here's the list of all 30, arranged by location (Courtesy of Ratchet.wikia.com):
Locations:
Oozla:
*Prehistoric Rampage - kill four Pterodactyls.
*Smash and Grab - obtained by destroying all breakables at the Megacorp store.
Maktar Nebula:
*Wrench Ninja: Blade to Blade - defeat Chainblade in the battle arena with only the wrench.
*Vandalize - destroy all breakables in the level, excluding the Thugs-4-Less Jamming Array area.
*2B or not 2B hit - defeat the B2 Brawler without being hit.
*Clank needs a new pair of shoes - win the jackpot from a Slot machine.
Endako:
*Destroy all breakables - break all the things that can be broken.
*Operate Heavy Machinery - kill 10 enemies with the crane.
Barlow:
*Speed Demon - finish a Hoverbike race in less than 2:10.
Notak:
*Planet Buster - destroy the floating globe in the Promenade area.
Siberius:
*You can break a Snow Dan - break the Snow Dan sculpture behind a garage.
Tabora:
*Heal your chi - find all the Desert Crystals in the dunes
Dobbo:
*Old Skool - defeat all the enemies with weapons from the original Ratchet & Clank.
Dobbo Orbit:
*Dukes Up - defeat the boss using only melee attacks.
*Robo Rampage - destroy all the objects on Lunar City.
Joba:
*That's impossible! - win the Impossible Challenge in the arena.
*How fast was that? - win a Hoverbike race with a completion time under 2:27.
*Wrench Ninja II: Massacre - defeat every enemy with only the wrench.
*Bye bye birdies - kill 12 birds.
Todano:
*Nothing to see here - destroy all four rockets on the Megacorp tour.
*You're my hero - protect all the tourists from the Mutant Test-Squirrels.
*Try to Sleep - turn 16 Mutant Test-Squirrels into sheep.
Boldan:
*No shocking developments - ride the grind rail without taking any damage.
Snivelak:
*Moving Violation - destroy 14 ships.
Damosel:
*Midtown Insanity - ride the Grindrail into the Hypnomatic without taking any damage.
*Safety Deposit - save all the Tourist Bots in the bank.
Grelbin:
*Be a Moon Child - collect all the Moonstones.
General:
*Nano to the max - max out Ratchet's Nanotech.
*Weapon Envy - collect and upgrade all the weapons (not including Mega or Ultra versions).
*Nice Ride - upgrade all parts of Ratchet's ship.