"determination against" is correct and can be used in written English.
It is generally used to express determination to oppose or resist something. For example, "The mayor showed determination against the proposed budget cuts."
On view is "Moved to Remember: Determination Against Hate Violence".
If there is an irrepressible human trait it's the determination, against all odds, to reconnect.
The response will be a renewed determination against international terrorism, several world leaders made clear yesterday.
"An attack of his kind has to reinforce our determination against the terrorist threat," he said.
Should there be an international determination against human-rights abuses in United States prisons?
This is our best weapon - we must show our determination against anything that may divide us.
In this version of history, the south went to war not to preserve the institution of slavery but to protect states' rights to self-determination against a federal government determined to impose its secular, cosmopolitan values on southerners' way of life.
It is the role of the state to defend individual self-determination against oppressive institutions, including religious institutions.
The Communist Party used to be very keen on "wars of national liberation," especially when they featured plucky Asian peoples struggling for self-determination against big, hegemonic bullies.
The Battle of Näfels culminated in a major victory for the Swiss Confederation in the first century of its struggle for self-determination against Habsburg overlordship.
It tells not simply the story of Albert Namatjira, but the story of a community seeking self-determination against enormous structural obstacles.
