SELECT 
  category_id, 
  parent_id 
FROM 
  jmj_categories 
WHERE 
  parent_id IN(
    100, 89, 92, 97, 36, 60, 83, 20, 109, 116, 
    26, 31, 104, 88, 106, 9, 69, 8, 67, 79, 
    47, 93, 80, 19, 68, 10, 21, 98, 90, 101, 
    32, 117, 30, 105, 70, 48, 45, 110, 84, 
    61, 2, 91, 94, 46, 111, 62, 99, 82, 25, 
    81, 11, 22, 33, 118, 3, 107, 27, 49, 85, 
    71, 102, 103, 4, 108, 34, 119, 28, 95, 
    112, 63, 23, 51, 12, 86, 96, 35, 29, 78, 
    73, 120, 50, 64, 113, 13, 24, 74, 65, 114, 
    5, 14, 121, 37, 52, 115, 15, 122, 53, 38, 
    75, 66, 54, 39, 16, 76, 77, 41, 57, 18, 
    59, 40, 17, 43, 55, 42, 56, 58, 44
  ) 
  AND category_id != 1

Query time 0.01075

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "29.42"
    },
    "table": {
      "table_name": "jmj_categories",
      "access_type": "ALL",
      "possible_keys": [
        "PRIMARY",
        "parent",
        "p_category_id"
      ],
      "rows_examined_per_scan": 120,
      "rows_produced_per_join": 120,
      "filtered": "100.00",
      "cost_info": {
        "read_cost": "5.42",
        "eval_cost": "24.00",
        "prefix_cost": "29.42",
        "data_read_per_join": "465K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ],
      "attached_condition": "((`jmj_test`.`jmj_categories`.`parent_id` in (100,89,92,97,36,60,83,20,109,116,26,31,104,88,106,9,69,8,67,79,47,93,80,19,68,10,21,98,90,101,32,117,30,105,70,48,45,110,84,61,2,91,94,46,111,62,99,82,25,81,11,22,33,118,3,107,27,49,85,71,102,103,4,108,34,119,28,95,112,63,23,51,12,86,96,35,29,78,73,120,50,64,113,13,24,74,65,114,5,14,121,37,52,115,15,122,53,38,75,66,54,39,16,76,77,41,57,18,59,40,17,43,55,42,56,58,44)) and (`jmj_test`.`jmj_categories`.`category_id` <> 1))"
    }
  }
}

Result

category_id parent_id
8 3
9 8
20 19
26 25
31 36
36 2
47 45
60 46
83 68
67 4
69 67
79 78
88 79
89 5
92 89
97 90
100 91
104 82
106 82
109 80
116 81
10 8
19 3
21 19
30 25
32 36
45 2
48 45
61 46
68 4
70 67
80 78
84 68
90 5
93 89
98 90
101 91
105 82
110 80
117 81
11 8
22 19
25 3
27 25
33 36
46 2
49 45
62 46
71 67
81 78
82 4
85 68
91 5
94 89
99 90
102 91
107 82
111 80
118 81
12 8
23 19
28 25
34 36
51 45
63 46
72 67
86 68
87 2
95 89
103 91
108 82
112 80
119 81
13 8
24 19
29 25
35 36
50 45
64 46
73 67
96 89
113 80
120 81
14 8
37 36
52 45
65 46
74 67
114 80
121 81
15 8
38 36
53 45
66 46
75 67
115 80
122 81
16 8
39 36
54 45
76 67
18 8
41 36
57 45
77 67
17 8
40 36
59 45
43 36
55 45
42 36
56 45
44 36
58 45