The first part of the battle is knowing your links. Each source of backlink information, including Google, has advantages and disadvantages. I have been resolving manipulative link issues for clients since 2011 (i.e. before Penguin) and what has worked in 100% of cases is a backlink report comprised of data from the following 5 sources: Google, Bing, AHREFs, Majestic and OSE. This combination of backlink data has always worked. That is not to say there are not other sources of backlinks which can be used.
Once you have a comprehensive list of all linking domains, the next step is to visit each site and determine if the links are manipulative or organic. Covering that topic fully would be a very lengthy article but in brief:
1. Closely examine Google's Quality Guidelines.
2. Remove any links you, or anyone else acting on the site's behalf (i.e. "SEO", link builder, developer, etc) built.
3. Remove links you created to the site from other sites you own
4. For each link ask "How did this link get here?" If the answer is the site owner independently created the link for their own reasons, that is great. This type of link is a naturally EARNED organic link. If there was any undue influence from the site owner which caused the link to be created, it is likely a manipulative link.
5. Take a look at the other links from that site. If the site offers links to other spammy sites, that is a very bad sign. Would you be ashamed for your customers to see this link?
6. Where is the link? Is it in content (which is strongly preferred) or is it in a sidebar or footer where spammy links are more likely to be found.
There is no hard and fast rules. There are guidelines. Ultimately you look at links and determine if they possess the qualities of an organic or manipulative link.
With respect to automated link identification services, there are two problems. First, they will typically identify some organic links as manipulative. Secondly, they will identify some manipulative links as organic. Both issues are highly problematic. You get what you pay for.
Good Luck.