Curse of Dimensionality : How many dimensions is too many dimensions?
As karthikeyan mg mention in his answer, you could use the explained variance score to get an idea of how many columns you can drop. Unfortunately, there isn't a magic number to know in advance. If you write code in Python, you should read this blog post in towardsdatascience.com

An Approach to Choosing the Number of Components in a Principal Component Analysis

After you rescale your data to 0-1, you can run this snippet of code and get a plot of variance loss for each components number you choose.

#Fitting the PCA algorithm with our Data
pca = PCA().fit(data_rescaled)
#Plotting the Cumulative Summation of the Explained Variance
plt.figure()
plt.plot(np.cumsum(pca.explained_variance_ratio_))
plt.xlabel('Number of Components')
plt.ylabel('Variance (%)') #for each component
plt.show()


This is the result from the blog post. As you can see, the variance starts to drop a lot after the 5 components. So, this number might be the one you could use.