Skilled worker visa is a point based category. You will need to score enough point to be eligible to apply under this category. You also need to score point of Maintenance and English Language requirement (Though you will automatically claim points for English Language as you must have completed your Bachelor or Masters degree in UK)You can switch into Tier 2 General if you are current leave is one of these categories:
student re-sitting an examination
student union sabbatical officer
Post Study work visa (Tier 1)
You can qualify to switch into Skilled worker visa BUT you must have lawfully obtained a UK bachelors or masters degree, postgraduate certificate in education or professional graduate diploma of education during your current or last permission to stay (period of continuous leave). This does not include, for example, vocational qualifications at degree level which are not degrees. All other Post Graduate diplomas are not acceptable for this purpose. If you are a PhD student, you do not need to have completed your course, but you must have completed at least 12 month’s study towards it in the UK.
Points For Your Attributes
You must score minimum 70 points and some characteristics are tradeable. You must be paid at least £25600 or the ‘Going Rate’ whichever is higher (there are some exceptions to this rule)
You can claim points for your education qualifications, salary, English language, your job offer, if you job code is in skill shortage category etc.