The venerable “Standings Repair Plan” by DeMichael Crimson is still handy:
And the United Standings Improvement Agency (USIA) is a service that can help also:
In general, it’s best to read mission text descriptions and check the Faction icons of whoever they’re sending you against as the objective. If it’s against a faction you don’t want to lose standings with, decline it. It’s best if you work from systems with multiple agents in them so you can get multiple options.