Question

Who has the power to dissolve legislative council?

Answer 1

The President has the power to dissolve the legislative council.

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Answer 2

The governor can dissolve the states legislative assembly only when the state is unable to function in conformity with the constitution of India. Even if the council of ministers of the union are threatened by the state government, they can't impose their whims through their agent, via the president.
The chief minister and the council ministers can advice the governor to dissolve the house, but to do they will have to prove not to have a majority in the house. If they don't it is well within the governor's power to reject such advice.
If the intent is malafied, the court will quash the dissolution. That is the dissolution of the house is subject to judicial review. The high court and the supreme court have the power to revive the state legislative assembly.
The legislative council of the state can't be dissolved. It's a permanent house analogous to the upper house of the parliament.