Note: work done by hired workers does count, however work done on contracted fields does not - you must own the field for the counter to increase. These achievements are also known to be slow sometimes, so you might have to do a little extra.Note 2: This must be done in a single save game, but is not limited to a single session
Fertilizing is spreading solid or liquid fertilizer. Slurry, digestate, and manure should count towards this. Herbicide probably not. It's possible that cultivating over oilseed radish will also count, but I had all my achievements way before I got into that. As far as "easiest" method, use a combo as noted below, or go with solid or liquid - it's much faster.
Note 3: Seeders and planters that fertilize at the same time may also count towards the fertilizing achievements
Along the way, you will have also unlocked: