In an arsenal at oracle have powerful tools of diagnostics of problems with a productivity....
additional lilnks :
I'm not sure if this is a good place but you may consider using Quest Toad, which is one of the most common SQL tuning tool. However, if you are interesting in SQL performance specifically to your DB, then you may consider SQL tuning packs that come with Oracle DB enterprise edition (beware if you are using standard edition).
Besides, Oracle has a very nice set of scripts allow you to download.... but you need to have an account in Oracle support:
SQL Tuning Health-Check Script (SQLHC) (Doc ID 1366133.1)
Can anyone share a tool for investigate SQL performance?
License agreements do NOT allow for sharing. You will need to get your own tool.
Start with the FREE sql developer from Oracle:
the best tool for investigating SQL performance is knowledge. A good starting point is the documentation. Google will turn up plenty of other resources. The rest is up to you to practice and learn.
Once you have an understanding of what performance tuning is, the actual choice of a tool to automate and streamline the process becomes a matter of personal choice. Any decent developer tool such as SQL Developer, TOAD or PLSQL Developer or management tools such as Enterprise Manager will provide plenty of features for performance tuning. The caveat is that it helps if you actually understand what they are presenting.