As of June 9, 2021, these are all the Base songs needed to complete the Played Everything! achievement. I have seen multiple threads on this; however, there has not been a complete list made. I have confirmed this list by playing and being a new owner with 13 hours at achievement time.

Thanks to @rob for making the initial list.

1. Rhythm Fighter
2. Bunny Robbie
3. Little Red Riding Hood's Daily
4. Call me baby
5. TWINKLE STAR
6. Magic Squirrel Party
7. Welcome!
8. εν.στει Διον.σια
9. NEKOPARA
10. I LOVE MY MOTOBIKE
11. MUSE DASH
12. TriColour Heartbeat
13. TriColour World
14. Sparkle-Weaving Rain
15. Ba-Miao-Zhi-Yu
16. Distant time
17. Canon in D
18. Journey
19. LALALA Refrain
20. Beyond The Horizon
21. ANGER FORCE - STAGE 4 –
22. Koi
23. Mr. Rabbit
24. Gaokao.Love.100Days
25. That Little Starry Sky
26. ICEY
27. SanRenHeZouGe
28. Tears
29. Candleman
30. Gothique Resonance
31. Platina
32. GAMEBOY
33. CN Parents
34. Lost Memories
35. Banner of the Maid
36. Relishing Rain
37. Bass telekinesis
38. Confession
39. Doom Disco
40. Solar Wind
41. The Mountain Eater
42. Nick of Time
43. Silver Town
44. Annihilator
45. Africa
46. When You're Away
47. Luo-Chen-Huan
48. Su-San
49. Deities of Cathaysia
50. NiLangQianQiu
51. HaiTangXian
52. Sunsetting Billows
53. RPG Theatre
54. I will be failed
55. You Are Right
56. Burn
57. OPUS: The Day We Found Earth
58. 8bit Adventurer
59. Journey (all lower case – there are two journey)
60. 8th Planet
61. Night of Full Moon

Have fun grinding!