Here is a list of the episode titles. From what I gather, the titles were changed a bit in the English dub.

Original Titles come first, then the English Dub titles are second, in italics:
01. Original Japanese Title (in english)
01. English Dub Title

First Season

01. First Time! Amazing! Stage
01. Amazing Stage Debut!

02. The Lonely Amazing Challenge
02. My Amazing and Lonely Challenge

03. The Distant Amazing Stage
03. The Amazing Distant Stage

04. Persevere for the Amazing Chance
04. Try Hard and You'll Get an Amazing Chance

05. The Always Amazing Distant Family
05. My Amazing Distant Family

06. The Small but Amazing Seal
06. The Amazing Seal

07. The Never Smiling Amazing Girl
07. The Amazing Girl Who Doesn't Smile

08. Suffering Amazing Star
08. An Amazing Star Even in Tough Times

09. Lead Role, the Amazing Challenge
09. My Amazing Challenge for the Lead Role

10. Lead Role, the Amazing Obsticle
10. Facing an Amazing Wall

11. Anna's Not So Amazing Father
11. Anna's Not So Amazing Father

12. Hot Amazing New Production
12. An Amazingly Hot New Production

13. Stormy Amazing Contest
13. The Amazing Competition Calls Up A Storm

14. The Mysterious Amazing Circus
14. Mysterious Amazing Circus

15. The Singing Princess's Amazing Love
15. The Diva’s Amazing Love

16. The Dark Amazing Rumor
16. An Amazing Sinister Rumor

17. Burn! The Amazing Mia
17. Fire it up! Amazing Mia

18. Yuri's Amazing Trap
18. Yuri’s Amazing Trap

19. The Family's Amazing Bond
19. Amazing Family Ties

20. From Zero, the Amazing Start
20. An Amazing Change from Zero to Hero

21. The Puzzling Amazing Masked Star
21. The Amazing Mystery Star

22. Under the Mask, the Amazing Resolution
22. The Amazing Resolve Beneath the Mask

23. The Mystical Amazing Act
23. The Legendary Amazing Maneuver

24. The Endless Amazing Intensive Training
24. The Amazing Intensive Training Continues

25. Two People's Amazing Partnership
25. An Amazing Bond

26. The Scar-Filled Amazing Revival
26. An Amazing Comeback

Second Season

27. The Star's Amazing Prologue (Part 1)
27.

28. The Star's Amazing Prologue (Part 2)
28.

29. It's a New Amazing Rival
29.

30. Another Amazing Rookie
30.

31. The Passionate Amazing Rival
31.

32. On the Icetop, the Amazing Confrontation
32.

33. In Sweat and Tears, the Amazing Rosetta
33.

34. After all, the Amazing Layla
34.

35. Marion's Amazing Debut
35.

36. Leon's Amazing Crash Course
36.

37. Two People's Amazing Demons
37.

38. The Angel's Amazing Counterattack
38.

39. It's a Cruel Amazing Festival
39.

40. The Hopeless, Amazing Return Home
40.

41. The Fresh Start's Amazing Decision
41.

42. The Humiliating, Amazing Co-Starring
42.

43. Boris's Amazing Proposal
43.

44. The Smiling Face's Amazing Departure
44.

45. Leon's Amazing Past
45. Leon's Amazing Past

46. The Fateful, Amazing Decision
46. The Amazing Fated Duel

47. The Swooping Flight of the Amazing Angel
47. Flight of the Amazing Angel

48. The Wounded Amazing White Bird
48. The Amazing Injured Swan

49. Each Amazing Tomorrow
49.

50. Not Avoiding the Super Amazing Combat
50.

51. To the Promise's Amazing Location
51.