The optimization process and recommendations:

1. Avoid Selecting Unnecessary Columns (query line: 2): Avoid selecting all columns with the '*' wildcard, unless you intend to use them all. Selecting redundant columns may result in unnecessary performance degradation.
2. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
3. Explicitly ORDER BY After GROUP BY (modified query below): By default, the database sorts all 'GROUP BY col1, col2, ...' queries as if you specified 'ORDER BY col1, col2, ...' in the query as well. If a query includes a GROUP BY clause but you want to avoid the overhead of sorting the result, you can suppress sorting by specifying 'ORDER BY NULL'.
4. Replace Join With Exists To Avoid Redundant Grouping (modified query below): When a joined table isn’t used anywhere other than in the WHERE clause, it's equivalent to an EXISTS subquery, which often performs better. In cases where the DISTINCT or GROUP BY clause contains only columns from the Primary key, they can be removed to further improve performance, as after this transformation, they are redundant.

Optimal indexes for this query:

ALTER TABLE `entries` ADD INDEX `entries_idx_id` (`id`);
ALTER TABLE `entries_keywords` ADD INDEX `entries_keywords_idx_entry_id_keyword_id` (`entry_id`,`keyword_id`);
ALTER TABLE `keywords` ADD INDEX `keywords_idx_id_key` (`id`,`key`);

The optimized query:

SELECT
        a.* 
    FROM
        entries a 
    WHERE
        (
            1 = 1
        ) 
        AND (
            EXISTS (
                SELECT
                    1 
                FROM
                    entries_keywords b 
                INNER JOIN
                    keywords c 
                WHERE
                    (
                        (
                            a.id = b.entry_id
                        ) 
                        AND (
                            b.keyword_id = c.id
                        )
                    ) 
                    AND (
                        c.key IN (
                            'wake', 'up'
                        )
                    )
            )
        ) 
    GROUP BY
        a.id 
    HAVING
        COUNT(*) = 2 
    ORDER BY
        NULL