When you have the need to find out real time what is causing high CPU issues within your Azure SQL Database, there is nothing better than using TSQL and SSMS. Azure portal will highlight the below, this is when I made CPU contention.

Some nice peaks, right?

This is the code you will need to find the query causing you a headache.

SELECT TOP 5 req.session_id, req.start_time, cpu_time 'cpu_time_ms', OBJECT_NAME(ST.objectid, ST.dbid) 'ObjectName', SUBSTRING(REPLACE(REPLACE(SUBSTRING(ST.text, (req.statement_start_offset / 2)+1, ((CASE statement_end_offset WHEN -1 THEN DATALENGTH(ST.text)ELSE req.statement_end_offset END-req.statement_start_offset)/ 2)+1), CHAR(10), ' '), CHAR(13), ' '), 1, 512) AS statement_text
FROM sys.dm_exec_requests AS req
CROSS APPLY sys.dm_exec_sql_text(req.sql_handle) AS ST
ORDER BY cpu_time DESC;
GO