There exists a continent on the scale of Eurasia, which spreads from tropical regions to polar. It has the full range of biomes that we find on Earth. On this continent, there are many varied wild beasts. All animals that are extant in the present day Americas may be found there, as well as all recently extinct animals on this list.
On this continent, there is only one type of 'magic,' and that is blood magic. A blood shaman gains his power by killing a beast and drinking the blood from his still beating heart. The animal must be killed with a sigil-blade called a blood knife, made from a special stone. This 'knife' can in fact be of any size, formed into a sword or a spear.
Once a blood shaman ritualistically kills a beast, he gains the power of the animal. Any strength, senses, or abilities of that creature can be utilized by the shaman; but there is no shape-shifting involved. Here are some examples and limitations.
Strength is gained by motion: If a shaman kills a bear, his punch will hit as hard as a bear's. If a shaman kills an alligator, his punch will hit as hard as an alligators (i.e. not that impressive). He will have an unbelievable bite force, but that may be hard to weaponize given the limitations of human teeth.
The shaman must have the 'parts' to gain the ability: A shaman who kills a deer can run 40 mph; a shaman who kills an eagle cannot fly, because he does not have wings. Similarly, a shaman who kills crocodile can't swim any faster, since a crocodile swims with its tail. But a shaman who kills a sea lion can, because a sea lion's flippers are just feet.
'Passive' abilities count: A shaman who kills a bison can stand, naked, in a blizzard for hours without trouble. A shaman who kills a camel can do without water for weeks. A shaman who kills a jaguar can move silently. Passive abilities don't depend on body part; you don't need a hump to go without water, or fur to withstand the cold.
The animal's final state is important: A wounded or trapped animal will not pass any of its powers on. This is important, since you cannot trap a beast in a pit, then kill it to claim its powers. The first strike on a healthy animal must be done with the blood knife or the blood magic will not succeed.
The abilities lose scale with the size of the animal: A 150 lb shaman that kills a 150 lb deer gains all of its speed and agility. A 150 lb shaman that kills a 15 lb rabbit gains at best 1/10 of its speed and agility. This doesn't work scaling up; a 150 lb shaman that kills a 15000 lb mammoth still gains only 100% of its abilities. It is considered shameful for a blood shaman to take the (meagre) powers of an animal much smaller than a human.
You only get the maximum of all animals you've killed: Killing two deer doesn't increase your speed twice. Killing a deer then a cougar only lets you take the best of either of their speed and agility.
Training to be a Blood Shaman is arduous. First you must master the spiritual powers needed to perform the rituals; then you must master the physical powers needed to kill your first beast. To ensure that this path is attainable, there is a standardized path of beasts you kill in a certain order as you ascend in skill at blood magic. What is this path?
Remember, there is no trapping or pre-wounding the animal. The first wound of the beast must be done with the blood knife, or the blood magic will fail.
The starting point is a plain old human with a knife/sword/spear, albeit one in fine physical condition. The ending point is the mighty mammoth. Few, if any, blood mages have ever attained its power.
The blood shaman must be expected to have at least even odds to kill each creature with only his blood knife. For example, if the last step was killing a cougar, it would be reasonable for the next step to be a horse, since cougars can kill and eat horses. If the last step was a deer, it would not be reasonable for the next step to be a bear, unless some special tactics were involved.
Biome is no limitation on order of animals. Tropical and arctic animals can be mixed in any order. Blood shaman are expected to span the continent in their lifelong quest.
The correct answer will get from human to mammoth in the fewest steps while never requiring the shaman to undergo unreasonable odds to kill another beast. A good answer will use the special abilities of one animal to tackle the next one in order.