public static void fire() {
    String requestId = insertEvents();
    if (requestId != null) System.enqueueJob(new FireQueueable(requestId));
}

public class FireQueueable implements Queueable, Database.AllowsCallouts {
    private String requestId;
    public FireQueueable(String requestId) {
        this.requestId = requestId;
    }
    public void execute(QueueableContext context) {
        if (fireFor(requestId)) {
            String nextRequestId = insertEvents();
            if (nextRequestId != null) System.enqueueJob(new FireQueueable(nextRequestId));
        }
    }
}

// Must use Database.AllowsCallouts for PDF generation
public with sharing class GenerateOnePDF implements Queueable, Database.AllowsCallouts {
    public void execute(QueueableContext context) {
        Blob v = Page.myPDFPage.getContentAsPDF();
        // Do your DML here.
    }
}

// Limit one enqueueJob per execute.
public with sharing class GeneratePDFFiles implements Database.Batchable<integer> {
    public Iterable<Integer> start(Database.BatchableContext context) {
        return new Integer[] { 1, 2, 3 }; // Change this logic as you like.
    }
    public void execute(Database.BatchableContext context, integer[] scope) {
        System.enqueueJob(new GenerateOnePDF()); // You'd pass your request ID, I suppose.
    }
    public void finish(Database.BatchableContext context) {

    }
}

<apex:page>
</apex:page>

public with sharing class GeneratePDFS implements Database.Batchable<Integer>, Database.Stateful, Database.AllowsCallouts {
    String priorId;
    Integer counter = 0;
    String insertEvents() {
        insert new Account(Name=counter.format());
            return ++counter > 5? null: counter.format();
    }

    public Integer[] start(Database.BatchableContext context) {
        return new Integer[] { 1 };
    }
    public void execute(Database.BatchableContext context, Integer[] scope) {
        if(priorId != null) {
            insert new Document(Name='Test Me', FolderId=UserInfo.getUserId(), Body = Page.myPDFPage.getContentAsPDF());
        }
        priorId = insertEvents();
    }
    public void finish(Database.BatchableContext context) {
        if(priorId != null) {
            Database.executeBatch(this);
        }
    }
}

public class FireEventsBatchable implements Database.Batchable<Integer>,
        Database.AllowsCallouts, Database.Stateful {

    // Entry point
    public static void execute(String requestId) {
        if (requestId != null) {
            Database.executeBatch(new FireEventsBatchable(requestId), 1);
        }
    }

    private String requestId;

    private FireEventsBatchable(String requestId) {
        this.requestId = requestId;
    }

    public Integer[] start(Database.BatchableContext bc) {
        // With batch size of 1 execute gets called up to 8 times
        return new Integer[] {1, 2, 3, 4, 5, 6, 7, 8};
    }

    public void execute(Database.BatchableContext bc, Integer[] scope) {
        if (requestId != null) {
            if (Events.fireFor(requestId)) {
                requestId = Events.insertEvents();
            }
        } else {
            System.abortJob(bc.getJobId());
        }
    }

    public void finish(Database.BatchableContext bc) {
        // If more to do - chain to another job
        execute(requestId);
    }
}