I will throw my 2 cents as I had to battle with exactly the same problem for presenting results for a 77x77 variables correlation matrix.
I tried just about anything you can think of in terms of conveniently visualizing a 77x77 matrix by using R, SPSS and Excel. From my experience, there is simply no magical pill/graph that will result in an 82x82 matrix (your dimensions), which can be easily visually digested, just due to too many variables being present. Now I resorted to employing the following strategy, which I thought was reasonable.
As you are, I was interested in showing highly-correlated pairs of variables. First, I looked through the literature to understand what is classed as a high correlation. Disclaimer: as with all rules of thumb, you should not blindly rely on such recommendations. Instead, take them as a starting point and then check papers/research in your respective field to determine/validate as to what is commonly thought to be highly correlated. For example, in the field of psychometrics, it is not uncommon to think that variables correlated as |.70| and greater are highly correlated. This is also supported by some more general published guidelines produced by Kenny.
Next, suppose you have chosen some criterion (e.g. |.70| or similar). Next, I resorted to writing an R code that will essentially give me the pairs of variables that adhere to this criterion (attached at the very bottom). Unless, everything in your correlation matrix is highly correlated, which I doubt by looking at the corrplot you attached, you end up with a neater and more manageable task. That is, now, the task can be reduced to producing only, for example, a 20x20 correlation matrix of only highly correlated variables.
At this point, let's backtrack just a little to counter a potential critique, as someone may say: "Yes, but what about showing other lower correlations amongst the remaining variables (as you cannot ignore non-high correlations)?" Again, due to the difficulties of presenting an 82x82 matrix in a visually digestible way, I would recommend to start presenting your results by describing the correlation matrix more generally, by noting a few key patterns. For example,
- Note dimensions of the correlation matrix.
- State proportion of positive/negative correlations.
- State proportion of variables that essentially showed no correlation; weak correlation; moderate correlation; and high correlation.
Give examples in each case (it is useful).
Now, at this point, notice how you ended your general summary of the correlation patterns with noting high correlations. From this point on, you can continue the flow and concentrate on the above, i.e. defining what you mean by high correlations and what made you consider a specific threshold to identify high correlations, then provide a more manageable and visually digestible corrplot of only highly-correlated pairs of variables. In addition to that, you may, optionally, rank-order highly correlated variables and present them in a simple table. From my presentation experience, it also looked very digestible and easy to follow. I will include a snapshot (note my table included extra metrics so I cut it and only attached a relevant part of the table; also my apologies for an over-sized picture, I could not figure out how to make it smaller).
### Identify highly-correlated pairs of variables
rm(list = ls()) # clean environment
library(foreign) # load packages
CORRECTED_cor <- cor(mydata) # cor matrix
CORRECTED_cor <- tbl_df(CORRECTED_cor) # tabulate cor matrix
CORRECTED_cor[lower.tri(CORRECTED_cor, diag = TRUE)] <- NA # remove lower triangle and diagonal elements
CORRECTED_cor[abs(CORRECTED_cor) < 0.70] <- NA # correlations below |.70| NA
sum(!is.na(CORRECTED_cor)) # only show cases with cor > |.70|
S <- which(abs(CORRECTED_cor) >= .70, arr.ind = T) # output rows and colums of correlations > |.70|
final <- cbind(S, abs(CORRECTED_cor[S]))
final <- tbl_df(final)
# Sanity check to make sure everything is correct
# Sort by increasing order
# Final dataframe sorted by increasing order
final <- arrange(final, V1)