General achievement guide: https://steamcommunity.com/sharedfiles/filedetails/?id=3573129260
Easter egg achievement guide: https://steamcommunity.com/sharedfiles/filedetails/?id=3652627204
Most of the achievements for winning a game in each mode can be sped up on the official servers if they're empty. Start a match either with or without bots and take the lead, then exit the server and quickly rejoin. The match should have automatically ended (unless there are other human players still on the server) and you will get credit for the win if your team is in the lead.
XP/level grind:
The fastest and easiest way to earn XP is to play Elimination on the map Testing Grounds against bots. Equip the AWP (press B to set your loadout) and head to the top of the nearest tower at the start of the match. Bots rarely go to the tops of the towers, so this is usually a safe spot to snipe enemies. Between matches, you can just press the "Ready" button to quickly repeat the same mode and map.
The XP earned in Elimination mode is as follows: 20 XP for each enemy that dies before you
10 XP for each kill
5 XP for each assist
20 XP for winning
The majority of the XP comes from surviving as long as possible, so that should generally be your priority. With this method, you can expect to get 200-300 XP per match with matches typically lasting no more than 1-2 minutes. Reaching level 64 requires a total of 102400 XP.