• Achelousaurus Friend
  Hatch a Achelousaurus
  
  
• Albertosaurus Friend
  Hatch a Albertosaurus
  
  
• Animantarx Friend
  Hatch a Animantarx
  
  
• Ankylosaurus Friend
  Hatch a Ankylosaurus
  
  
• Apatosaurus Friend
  Hatch a Apatosaurus
  
  
• Brachiosaurus Friend
  Hatch a Brachiosaurus
  
  
• Gastonia Friend
  Hatch a Gastonia
  
  
• Gigantspinosaurus Friend
  Hatch a Gigantspinosaurus
  
  
• Kentrosaurus Friend
  Hatch a Kentrosaurus
  
  
• Lambeosaurus Friend
  Hatch a Lambeosaurus
  
  
• Mamenchisaurus Friend
  Hatch a Mamenchisaurus
  
  
• Minmi Friend
  Hatch a Minmi
  
  
• Ornithomimus Friend
  Hatch a Ornithomimus
  
  
• Oviraptor Friend
  Hatch a Oviraptor
  
  
• Parasaurolophus Friend
  Hatch a Parasaurolophus
  
  
• Seismosaurus Friend
  Hatch a Seismosaurus
  
  
• Shantungosaurus Friend
  Hatch a Shantungosaurus
  
  
• Spinosaurus Friend
  Hatch a Spinosaurus
  
  
• Stegosaurus Friend
  Hatch a stegosaurus
  
  
• Styracosaurus Friend
  Hatch a Styracosaurus
  
  
• Triceratops Friend
  Hatch a Triceratops
  
  
• Tyrannosaurus Rex Friend
  Hatch a Tyrannosaurus Rex
  
  
• Velociraptor Friend
  Hatch a Velociraptor

Good news! You don't need to get the 4th 'extra' rocket to earn these achievements, so you can take as long as you need in each park without worrying about a time-limit. There's actually no achievement at all for getting the extra 4th rocket ships.

• Toronto
  Earn 3 Rocket Ship Parts in Toronto
  
  
• Abandoned
  Earn 3 Rocket Ship Parts in Abandoned
  
  
• Tropical Islands
  Earn 3 Rocket Ship Parts in Tropical Islands
  
  
• Energy
  Earn 3 Rocket Ship Parts in Energy
  
  
• Beach Resort
  Earn 3 Rocket Ship Parts in Beach Resort
  
  
• Health
  Earn 1 Rocket Ship Part in Health
  
  
• Privacy
  Earn 3 Rocket Ship Parts in Privacy
  
  
• Machu Picchu
  Earn 3 Rocket Ship Parts in Machu Picchu
  
  
• Breeding
  Earn 3 Rocket Ship Parts in Breeding
  
  
• Pyramids
  Earn 3 Rocket Ship Parts in Pyramids
  Tip: Click on the tops of the big pyramids to uncover the hidden dino rocket ships. The in-game directives aren't very clear that this is what you need to do to complete the task and I've seen lots of people get stuck by this in the discussion boards.
  
  
• Space
  Earn 3 Rocket Ship Parts in Space
  
  
• Breakout
  Earn 3 Rocket Ship Parts in Breakout
  
  
• Ranch
  Earn 3 Rocket Ship Parts in Ranch
  
  
• Return Home
  Earn 3 Rocket Ship Parts in Return Home

The theme items are expensive ($50K each) which is the only thing that will slow you down here. Click on an exhibit, set a "theme" and then review the requirements. You must set a thee, meet all the requirements AND have the theme item in exhibit.

Build an exhibit with a Prehistoric theme

• Meet size requirements
  
• All plants require water
  
• Realism must be at maximum (Unlock the Forest Pack, Mud Pack, and Sand Pack to access the prehistoric plants to meet this requirement. Plants will then show up under Trees/Bushes as Tier 2 plants)
  
• Volcano theme item

Theme bonus

• 30% more appeal in this exhibit
  
• Dinos in this exhibit do not become sick
  
• Volcanos are active in this exhibit

Build an exhibit with a Secure theme

• Meet size requirements
  
• All plants require water
  
• All fences must be at maximum strength
  
• Security Camera theme item

Theme bonus

• 20% more appeal in this exhibit
  
• Stronger fences
  
• Alarms activate when dino is loose

Build an exhibit with a Organic theme

• Meet size requirements
  
• All plants require water
  
• Have perfect Biodiversity
  
• Windmill theme item

Theme bonus

• 30% more appeal in this exhibit
  
• Poop disappears
  
• Butterflies appear in this exhibit

Build an exhibit with a Eden theme

• Meet size requirements
  
• All plants require water
  
• No viewing spots
  
• Mother Tree theme item

Theme bonus

• 20% more appeal in this exhibit
  
• Happiness requirement for Dino Nest is much lower
  
• Rainbows appear in this exhibit

Build an exhibit with a Spooky theme

• Meet size requirements
  
• All plants require water
  
• Only carnivores in this exhibit
  
• Skull Tree theme item

Theme bonus

• 20% more appeal in this exhibit
  
• 30% more donations from this exhibit
  
• Fog appears in this exhibit

Build an exhibit with a Magical theme

• Meet size requirements
  
• All plants require water
  
• Only herbivores in this exhibit
  
• Magical Tower theme item

Theme bonus

• 20% more appeal in this exhibit
  
• Dinos require less food
  
• Fireflies appear in this exhibit

These hidden achievements were added with the DLC. Literally, all you need to do is buy the DLC and then play the 3 new parks.

• Shipyard
  Earn 3 Rocket Ship Parts in Shipyard
  
  
• Factory
  Earn 3 Rocket Ship Parts in Factory
  
  
• Fire Party
  Earn 3 Rocket Ship Parts in Fire Party

If you're going to run into trouble unlocking an achievement, it's probably going to be in the below list as a few of these are quite challenging.

• Eureka!
  Make your first science discovery
  
  
• Job Creator
  Employ at least 10 people
  
  
• Mini Madness
  Have 50 guests in your park at once
  
  
• Busy Bee
  Have 100 guests in your park at once
  
  
• First Steps
  Have your park operating for 1 year
  
  
• Perfection
  Create a perfect Habitat for one of your Dinos
  Tip: Make sure the habitat size is big enough for the amount of dinos inside. Place enough food and toys. Have the correct type & amount of Trees, Bushes, and Rocks. Have a mate of the opposite sex. Place plenty of tall grass for hiding, as well as, using fencing with higher privacy rating to reduce dino stress.
  
  
  These are going to require more intentional effort.
  
  
• Elated
  Sell 1000 balloons
  Tip: Lower the cost of the balloons and have plenty of shops placed in each park. After that all you can do is wait. There's no way to know how far or close you are to unlocking this one unfortunately.
  
  
• Heaven is a Place on Earth
  One of your Dinos achieves 100% Happiness
  
  
• Parkasaur
  Achieve 5 star rating in a park
  
  
• Dino Friend
  Achieve 30,000 Dino Appeal in a park Tip: You will unlock this on your way to unlocking the Dino Tycoon achievement
  
  
• Dinosaur Tycoon
  Complete the Dinosaur Tycoon challenge
  Tip: From the initial home screen, select the Customize section, then under the Mode dropdown you will find Dinosaur Tycoon. You need to achieve a Park Appeal of 50,000 + have 300 guests. This is basically the game on HARD MODE as supplies have higher prices and dinosaurs needs are more demanding.
  My advice is to focus on breeding dinos with higher appeal.
  
  • Unlock the Dinosaur Nest, DNA Machine, and Chrono Eggcelerator. Place the later 2 anywhere in the park.
    
  • Place at least 2 dino eggs in an exhibit. You'll need to pay close attention to the eggs. You need to click the eggs when they are developing but NOT ready to hatch. If they are ready to hatch, you've missed your chance to upgrade the stats.
    
  • Once eggs have been laid, make sure you have a female and a male. Click an egg to check the sex, you can change the sex of an egg from the Scan tab.
    
  • At the top of the egg window, there are 3 empty boxes (1 white and 2 blue). In the blue boxes, place a Rare Gem and a hat with high +Appeal (FYI, placing a hat in the white box of an egg will change the Primary color of the dino).
    
    • The Coyboy hat is a rare drop with +160 Appeal.
      
    • The Wizard hat is a rare drop with +120 Appeal and No Poop feature.
      
    • The Mushroom hat can be bought at the hat store and has +80 appeal and the friendly status.
      
    • The Kimmy hat is the same as the Mushroom hat but is acquired from digging.
  • Hatch the egss and remove the adult dinos from the exhibit, then wait for the babies to grow up and put hats with high appeal on them.