value = dct['alerts'][0]['status']
としたら如何でしょうか。
質問文の['alert']は['alerts']のミスではありませんか。
以下にipythonの結果をのせておきます。
ipython
1In [1]: dct = {"alerts":
2 ...: [
3 ...: {"id":"3XXXXXXX","status":"CRITICAL","monitorId":"3XXXXX","type":"connectivity","ope
4 ...: nedAt":1535526664,"hostId":"3XXXX"
5 ...: }
6 ...: ]
7 ...: }
8 ...:
9
10In [2]: dct
11Out[2]:
12{'alerts': [{'hostId': '3XXXX',
13 'id': '3XXXXXXX',
14 'monitorId': '3XXXXX',
15 'openedAt': 1535526664,
16 'status': 'CRITICAL',
17 'type': 'connectivity'}]}
18
19In [3]: dct['alerts']
20Out[3]:
21[{'hostId': '3XXXX',
22 'id': '3XXXXXXX',
23 'monitorId': '3XXXXX',
24 'openedAt': 1535526664,
25 'status': 'CRITICAL',
26 'type': 'connectivity'}]
27
28In [4]: dct['alerts']['ststus']
29---------------------------------------------------------------------------
30TypeError Traceback (most recent call last)
31<ipython-input-4-fbe317a82bfe> in <module>()
32----> 1 dct['alerts']['ststus']
33
34TypeError: list indices must be integers or slices, not str
35
36In [5]: dct['alerts'][0]
37Out[5]:
38{'hostId': '3XXXX',
39 'id': '3XXXXXXX',
40 'monitorId': '3XXXXX',
41 'openedAt': 1535526664,
42 'status': 'CRITICAL',
43 'type': 'connectivity'}
44
45In [6]: dct['alerts'][0]['status']
46Out[6]: 'CRITICAL'
47
48In [7]: