Bots / Robots bombard my web site (In search)

Try reviewing:
https://help.dreamhost.com/hc/en-us/articles/216105077-How-can-I-control-bots-spiders-and-crawlers-

Try my plugin Pareto Security too, it does pretty well with reducing bots [In advanced mode/Hard Ban Mode].

@t-p ; Already tried. It does not work.

@te_taipo ; Now I tested it and it does not work.

Sorry I just saw the attachment you posted and yes, these would not be prevented by Pareto Security. They appear as a legit search request except for the fact that the requests are rapid and close together from a multiple list of IP addresses amounting to a denial of service attack.

You could have a look through some of the plugins that disable the search function for now as a possible means of alleviating the stress on the server until you work out a better solution.

You would then also need to prevent page execution of the search via HTACCESS as well else the search request while using less server resources, would still amount to a default page load of the index.php file.