How to delete multiple save files in Xcom2 on the PS4?
In my current campaign I don't shy away from save-scumming.
On the PS4, I am only allowed to have 100 save files. In order to delete old ones, I have to select each entry in the savegame list and hit delete for each entry. This is a bit tedious, esp. since the deletion of one savegame takes a while.
Is there a way to bulk-delete old save-games?
Looks like you've beein using XCOM's in-game menu to delete these saves. Don't. As you said, this is tedious and really slow. You might want to use the PS4 system's feature to bulk-delete these files, and without having to wait in between.
Your save files can be found in PS menu > (Settings) > [Application Saved Data Management] > [Saved Data in System Storage] > [Delete] > XCOM2
If you want to delete only a limited number of files, go to this folder and select all unwanted saves before deleting your selection. You can also do it the other way and 'select all' files before unselecting the files you DON'T want erased. Depending on how many saves you intend on deleting / keeping, this might be the fastest option. In both cases, you might want to give a special attention to your Profile and Character pool.
Once you have selected all undesired files, hit the 'delete' option. No need to wait in between two files but you'll still have to handpick them and wait during deletion. No automatic way that I know of, unfortunately.
Also, as stated by Steve-O in comments, XCOM2 has a pretty useful auto-save feature which will create 3 disctinct files and overwrite the oldest one every combat round. This provides a recent file loading option in case of unwanted events in combat while not flooding your system with tons of saves. Note that this will only cover the 3 lasts rounds, though.
Finally, if you still want to keep more than 100 saves, you might want to upload (via PS+) or copy (via USB key) the files you want to save (see official guide), and wipe all saves from your PS4 (once again, be careful of your Profile save and Character pool save). You can always download or copy back necessary data later.