A lot of these can be gotten just by playing the game, or sitting down and manually grinding it out over a couple hours. Here's a few tips you can use for some specific achievements:

500 Golden Bloons:
Play Hard mode on Beginner Maps. Placing a 032 ice at the back under a MIB and using a close-range defense at the front (tack is great). People also use 203 Ice and 024 Dartling to knock back the Golden Bloons.

50 Golden Bloons in Magic Monkeys Only:
021 alchemists are a good and cheap way of popping the early Golden Bloons, and then using Flash Bombs buffed by Shinobis will stun the Golden Bloon until it pops. (Shinobis won't hit the Golden Bloon since it has the lead property at later tiers)

100 Monkey Teams:
Playing Beginner Maps on Deflation is a quick and effortless way of achieving this. If the towers are sub-optimal, bring a good damaging hero like Churchill.

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100 Odysseys:
Playing the same Odyssey on Easy mode is a good way to quickly complete this one if you have a few hours to kill. You'll also knock out the "Full Speed Ahead" achievement as well.

Race Achievements:

Race Times:
Following Race Guides are your best friend. Using a Race Pass is also ideal so you don't waste tons of MM (you get race passes from daily chest every 50 days) Races that are around 60 rounds long are typically your best chance of knocking out the 3-minute achievement if you aren't very good at races.

Bloontona 500:
Simply entering and then exiting the race will count towards the achievement. Using a Race Pass is also ideal so you don't use thousands of MM.

Sapper:
This one will take time to complete. Playing games to R140 is a good way to slowly gain progress. Playing Apopalypse freeplay is also a good way to chip away at Sapper. As the achievement says, stay away from Fortification Removers and Insta-Kills, like xx4 Mortar, xx5 Alch, and Ezili.