Azure SQL Alter compatibility level Strategy
But 120 and 130 are pretty old. 160 is the latest and greatest.
What strategy you should apply depends a little on what your concerns are. Functionally, there are not that many breaking changes, although there are a few marginal ones you could run into.
More likely is that run into performance issues, because you get a new version of the optimizer and there are queries for which the intended improvement backlashes. Query Store is your friend here. If this happens, you can find the query in Query Store and force the old plan, until you have analysed the query in more detail.
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