Medium Puzzles 

Workings

Hint
Calendar.

Answer
Dragon.

From the Chinese calendar in reverse order.

Workings

Hint
Try writing the numbers out as letters.

Answer
45.

Reasoning
Each term increases by the number of letters in the previous term (ignoring any hyphens).
1  + length("ONE")       = 4
4  + length("FOUR")      = 8
8  + length("EIGHT")     = 13
13 + length("THIRTEEN")  = 21
21 + length("TWENTYONE") = 30
30 + length("THIRTY")    = 36
36 + length("THIRTYSIX") = 45

Workings

Hint
A very common sequence, but in base 8!

Answer
13.

Odd numbers expressed in base 8, 11 in base 8 = 13.

Workings

Hint
Look at the gaps in the alphabetic position.

Answer
V.

Skip three and two letters alternately.