The online achievements have to do with your performance against the rest of the players that take part in each event. Kicking things off, the Competitive part of the game as its online mode is called is separated into two parts, the Pro Tour and the Community Events. Each time you want to take part in any type of competitive event, you need to keep in mind that you're competing against players on the same handling style as you.
The Pro Tour features a specific car class each day and players can get promoted to a higher tier (and then division) if they perform good enough. Here we have rally stages, where all participants that get matchmade to one another run each stage at the same time. Since the game's population is very small nowadays and the mode itself was never popular at all, you'll need to grab three of your friends and try to get matchmade together. You can unlock the following two achievements this way:
Up and up
Get promoted to a new Tier in Pro Tour
You start off right at the bottom, which is Tier 7 of Division 3. You need to get promoted to Division 3 Tier 6 to unlock "Up and Up" and that's done by getting +7 points. The plus sign is there since losing or doing mediocre in an event will have you lose points if we assume that there's 4 of you competing each time. Therefore, get matchmade with your friends or other people using a Gaming Session here on TrueAchievements.com and settle on a single finishing order. Keep that order going until the person who won all the stages unlocks the achievement. That person then goes 4th, while everybody else gets bumped up one spot. Eventually all four will get the achievement.
With all participants finishing the stages and not quitting, everybody works towards "Sweaty" at the same time:
Complete 25 Events in Pro Tour
After everybody has unlocked "Up and Up", you need to complete the events as fast as possible, so running normally to see who's the fastest is the best method in order to complete the rest of the events needed for "Sweaty".
Moving on to the community events, we have several ones that reset every so often, where you need both skill and luck to unlock their respective achievements. Starting off with the Daily events, there are two of them each day, the "regular" Daily Event and the Delta Daily which comes in less often. Both events have an achievement associated with them and work similarly. You need to post a time that's good enough compared to the rest of the participants in order to finish the event in a certain tier.
The Day Today
Finish in the Second Tier or higher in a Daily in Community Events
The Day Today is unlocked if you finish a regular Daily Event in Tier 2 or higher (Tier 1), which is basically in the top 50%. There are not restarts in any of the community events, so you only get one run and that's it. Rather than pushing as hard as you can, it will be much easier to be consistent around the 40-50% mark if you back off the throttle and make sure you don't crash and don't get penalized. Since this event resets every day, you'll get many chances to get this achievement.
Finish in the Top Tier of a Delta Daily in Community Events
Delta Force is unlocked by finishing in the top 50% (there are only two tiers here) in a Delta Daily event. The situation here is the same as before, don't push like a madman and you'll be fine. Sometimes Delta Dailies won't be available, but keep checking every day and one will appear before long.
The Flavor of the Week achievement is unlocked by finishing a Weekly Event in two successive weeks. There are always two weekly events going on and you can pick whichever you like and complete it, DNFs won't help here. Each Weekly Event consists of a few stages, so it's an hours worth of driving give or take. There is no delta goal here, so make sure you make it to the end. You'll need to complete the event, return the very next Monday to receive your credit reward and do the next one before the following Monday. The achievement was glitched up until April of 2018 or so and the description is 100% misleading, but that's how this achievement is unlocked. Credit goes to TA user "szogyenyi1993" who confirmed the requirements and posted the respective solution (which initially required both Weeklies in a given week to be completed, so 4 events in total) and "Trutch" for confirming only one Weekly per week is required as of May of 2019.
Finish a Stage in sunny conditions in Community Events
Taps Aff (like "tops off" but with A's instead of O's) requires you to complete a stage in sunny conditions in any Community Event. A stage features sunny conditions if the weather symbol is (you guessed it) a sun, without any cloud icons. In order to save time, leave this for last, since you'll be going through a significant number of stages in your attempt to unlock all of the other achievements from the Community Events.
Complete all 12 Stages of a Monthly Event in Community Events
The Monthly Event is the longest event in the Community Events, but just like the Weekly, the achievement associated with it doesn't require you to complete a delta goal. Just casually drive to the end of it, which will come after 12 stages and the achievement is yours. Like before, be mindful of the lack of restarts, so keep it as clean as possible to minimize the chances of you suffering a part failure. DNFs don't count once again.
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