Being first boss one might be caught unprepared for this one. It is heavy, and I think it has most health from all bosses, even as it is only first of them.
Tsar Tank is last to come in this map, so you have time to accumulate best possible defence for it. During it's ride towards your Toy Box it stops occasionally dropping infantry which starts rushing forward. There is usually around 30-40 infantry coming, so you must be prepared to take care of those too, or you will lose even if you are prepared for Tsar Tank.
Route this boss takes start from far left corner of map. It then moves at back of map to right side, and come down by road towards your defences. It will crush your first turret defence (simply rides over it, and that's end of it story). It then turns towards your Toy Box and rides along road to it. Infantry is dropped right at begining first time, second time when it has reached right side, then when it is just at your turrents on right side, then 2-3 times when it goes between your defence line.
Howlitzers are practically only thing which damage Tsar Tank, and you need lots of those. Most of waves in this level are infantry, so you can do quite fine with just some chemicals at strategic locations, and then having rest Howlitzers. When Tsar Tank arrives, remember to aim your cannons towards it (if they ain't positioned properly yet). And when it moves past you, turn your cannons once again towards it. Amount you need these cannons vary a bit. Two is most likely too little, with three you might just do it without sweat and chance for big mistakes. 4-5 cannons should be good, but having more doesn't hurt.
Keep some fences on that road, between your defence lines. That'll slow down infantry this boss drops, and your left over defences can take care of them even without howlitzers help.
If Tsar Tank get between your defence lines, your howlitzers might stop firing, as it is too close. Take control of one of those by yourself, and just keep shooting towards it. It is so big that you'll hit it anyway, even as it's too close for AI to do shooting.