I'd suggest two basic additions to the scenario to make this a complete hunting tutorial:
1) add in parrots for the reasons stated above
2) since every other animal is dealt with in this scenario, you might as well make a Giant Spider/Spider Pen objective (to make it different to the other objectives, only put baby spiders on the map so the player has to grow the spider first)
A few suggestions to spice this scenario up (as it is rather boring):
1) Change the Aegean Isles into an archipelago. Set it up like the Galapagos, with each island having a unique biome and the relevant animals (with some redundancy, so it is not just one animal per island). Sprinkle in some dens on the starting map, so new players get to see them (I saw none when I played). Allow players to build basic ships obviously.
2) Add in some competition so it becomes a race of sorts, as previously suggested. Have the race develop in multiple stages (GM first, then other animal objectives). To keep it easy, maybe require that the player only wins a certain number of the races (but they still have to complete each objective before the next race starts). Maybe the GM race counts for 2-3 points so that it is the most important, and the rest count for 1 point. You win if you have more points than your opponent (maybe displayed to the player via mood bonuses, +1 - You were the first to bring me an Elephant).
3) Split up the starting areas away from the Isles. Maybe Keelyn and your competition start on a sliver of a continent, and you start on an island off the mainland. Your first objective could be to sail to Keelyn to get your mission. Sailing back and forth from the Isles could add a level of risk, as your low level ships compete with sea creatures to get the animals back safely (the first time you sight each sea creature, a pop up describing it could come up). Having a bunch of sea creatures around the Isles could add to their mystique and feeling of remoteness too.
4) Have open borders with Keelyn and build the cages in her city. That way, she builds the GM, not you (which also solves the extra trophy issue and makes players want to build the GM themselves in a regular game even more, as they never get to build it in this scenario). You might have to give Keelyn two cities in order to make the race with the other civ work (you have to get cages and the GM built in city A, your competition has to do it in city B).
5) To make the race part even more exciting, add in a race against time for the second phase (post GM phase). Give Keelyn's city/cities only a few hammers, so the GM builds slowly. Once she starts building, you get a pop up where she tells you she wants to throw a grand opening party for the GM. She needs silk for the performers' costumes and she wants an elephant for the show as well. You have to gift her an elephant and get a baby spider, grow it to a giant spider and build a silk pen in the city with the GM before she finishes the GM (if you manage to do it in time, she gets a bunch of hammers and finishes the GM on the next turn). You could leave the Griffon as a third, untimed phase (after the great party [or, if you failed the second phase, after you get her both items], she comes to you and says she feels the GM is incomplete and wants a Griffon to add to her collection).
I think the above suggestions would preserve the tutorial nature of this scenario, but make it MUCH more interesting and fun to play, as well as feel more immersed in the lore.