By forced move, it is meant that the player has only one legal move.
[fen "7k/q5Q1/p4PPK/6PP/8/5P2/8/8 b - - 0 1"]
1... Qxg7+ 2. fxg7+ Kg8 3. f4 a5 4. f5 a4 5. f6 a3 6. f7#
Above is an example with 10 half-moves. Each half-move is the only legal one and the end is a checkmate.
If you don't mind a bushel of promoted Queens, you can get 14 half-moves . . .
[Title "14 forced half-moves to checkmate"]
[Fen "3b3k/qqqqq3/rr4NK/7R/5N1Q/7Q/B6Q/7R b - - 0 0"]
1... Rxg6+ 2. Nxg6+ Rxg6+ 3. Kxg6+ Qh7+ 4. Rxh7+ Qxh7+ 5. Qxh7+ Qxh7+ 6. Qxh7+ Qxh7+ 7. Qxh7+ Qxh7+ 8. Rxh7#
The longest known sequence, aka the record length, is 16 plies. I obtained this problem from the Die Schwalbe Chess Problem Database. It can be also be viewed on page 13 in a PDF of the original source.
[Title "Bernd Schwarzkopf After Karl Scherer, Feenschach 1980, Mate In 8"]
[FEN "1KN4r/QRRRRRRr/kq6/p1q1R3/PP1q1b2/4q3/5q2/1r4q1 b - - 0 1"]
[startflipped ""]
1... Qxa7+ 2. Rxa7+ Qxa7+ 3. Rxa7+ Qxa7+ 4. Rxa7+ Qxa7+ 5. Rxa7+ Qxa7+ 6. Rxa7+ Qxa7+ 7. Rxa7+ Rxa7 8. b5+ Rxb5+ 9. axb5#
If only discovered checks are allowed, here is a sequence of 6 plies, as the first move doesn't count. I found it on Tim Krabbe's website in Diary Entry #265. The composer's first name comes from the problem's entry in the Die Schwalbe Chess Problem Database.
[Title "Vladmir Korolkov, 1940, White Wins"]
[FEN "6B1/5Nb1/3p4/q2krP1R/Nn2p3/pPKnr3/Q1PB4/3R4 w - - 0 1"]
1. Nd8+ Re6+ 2. f6+ Ne5+ 3. Bxe3+ Nd3+ 4. b4#
Here's a game from 1912 between Edward Lasker and George Alan Thomas. All blacks moves are forced.
[fen "rn3rk1/pbppq1pp/1p2pb2/4N2Q/3PN3/3B4/PPP2PPP/R3K2R w KQ - 20 11"]
1... Qxh7+ Kxh7 Nxf6+ Kh6 Neg4+ Kg5 h4+ Kf4 g3+ Kf3 Be2+ Kg2 Rh2+ Kg1 Kd2# 1-0
In answer to your question, I'm sure there's an even better hypothetical board position, but this was a really game played by competent players all be it in a casual setting.
Sources:
This answer is only the longest forced checkmate, because I missed your condition that each half move be the only legal move for both sides. The following is a forced checkmate in 262 moves (if both sides play perfectly).
[fen "6k1/5n2/8/8/8/5n2/1RK5/1N6 w - - 0 1"]
1. Kd3 N3g5 2. Kd4 Ne6+ 3. Kd5 Nc7+ 4. Kc6 Ne6 5. Kd7 Nfg5 6. Kd6 Kg7 7. Ke5 Nc5 8. Kf5 Nge4 9. Ra2 Nd6+ 10. Ke5 Nf7+ 11. Kd5 Nd3 12. Kd4 Nb4 13. Ra4 Nd8 14. Kc4 Nbc6 15. Kd5 Ne7+ 16. Kd6 Ng6 17. Ra8 Nf7+ 18. Ke6 Nf8+ 19. Kd5 Ng6 20. Ra6 Nf4+ 21. Kd4 Nd8 22. Nc3 Nde6+ 23. Ke3 Ng2+ 24. Kf2 Ngf4 25. Kf3 Kf7 26. Ra7+ Kg6 27. Ke4 Kg5 28. Ra5+ Kg4 29. Ke5 Nc5 30. Nd1 (30. Rxc5??... Nd3+ 31. Kf6 Nxc5 32. Ne2 Ne4+ =) Ng6+ 31. Kd5 Nb3 32. Ra2 Nf4+ 33. Ke5 Nc5 34. Ne3+ Kf3 35. Ra3 Ng6+ 36. Kd5 Nd3 (37.Rxd3??... Nf4+ = 38.Kc4 Nxd3 39.Kxd3) 37. Kd4 Nde5 38. Ra6 Nf4 39. Nf1 Nf7 40. Rf6 Ng5 41. Ke5 Ngh3 42. Rf7 Ke2 43. Ng3+ Ke3 44. Nf5+ Kf3 45. Nd6 Ke3 46. Nc4+ Kd3 47. Nb2+ Kc2 48. Na4 Nd3+ 49. Kd4 Ng5 50. Rd7 Ne6+ 51. Kd5 Ng5 52. Rg7 Kb3 53. Nb6 Nb4+ 54. Ke5 Nd3+ 55. Kf5 Nh3 56. Rc7 Nb4 57. Rc8 Nf2 58. Nd7 Nc2 59. Nc5+ Kb4 60. Ke5 Ng4+ 61. Kf4 Nge3 62. Nd3+ Kb3 63. Nc1+ Kb4 64. Ke4 Nc4 65. Rg8 Nb6 66. Rg2 Na3 67. Rb2+ Kc5 68. Nd3+ Kc6 69. Rg2 Na4 70. Rg5 Nc3+ 71. Ke5 Na4 72. Ke6 Nb5 73. Nb4+ Kb6 74. Nd5+ Ka5 75. Rh5 Nc5+ 76. Ke5 Nd3+ 77. Ke4 Nc5+ 78. Ke3 Na6 79. Rh1 Nbc7 80. Nf4 Kb4 81. Kd4 Nb5+ 82. Ke5 Nc5 83. Nd5+ Kb3 84. Rh3+ Kc4 85. Rh4+ Kd3 86. Nf4+ Kd2 87. Rh2+ Kc3 88. Kd5 Kb4 89. Rh4 Na4 90. Nd3+ Kb3 91. Rg4 Kc2 92. Nf4 Kd2 93. Rg7 Ke3 94. Ng2+ Kd2 95. Rh7 Nb2 96. Rd7 Ke2 97. Rb7 Nd1 98. Kc5 Nbc3 99. Kd4 Kd2 100. Rd7 Ke2 101. Nh4 Nb5+ 102. Kc4 Na3+ 103. Kb3 Nb1 104. Nf5 Nf2 105. Kc2 Na3+ 106. Kc3 Nb1+ 107. Kd4 Nd2 108. Re7+ Kf3 109. Rf7 Nh3 110. Nd6+ Ke2 111. Re7+ Kf3 112. Re3+ Kg4 113. Ra3 Nf1 114. Ra4 Ng5 115. Ke5+ Kf3 116. Nf5 Nd2 117. Ra3+ Kf2 118. Ra2 Ke2 119. Kd4 Nge4 120. Ne7 Kf3 121. Nd5 Nb3+ 122. Kc4 Nc1 123. Ra3+ Kf2 124. Ra8 Ne2 125. Rg8 Ng1 126. Kd4 Nd6 127. Ke5 Nc4+ 128. Ke4 Nd6+ 129. Kf4 Ne2+ 130. Ke5 Nb5 131. Rf8+ Ke1 132. Rd8 Nbc3 133. Nb4 Kf2 134. Nc2 Nc1 135. Rc8 Nb5 136. Rb8 Nc3 137. Rd8 Ke2 138. Kd4 Nd1 139. Na1 Kd2 140. Ke4+ Ke2 141. Rc8 Nf2+ 142. Kd4 Ncd3 143. Nb3 Nf4 144. Rg8 Kf3 145. Nd2+ Ke2 146. Nc4 Kf3 147. Ne5+ Ke2 148. Re8 N2h3 149. Nc4+ Kf3 150. Ra8 Ng5 151. Ra3+ Ke2 152. Ke5 Nd3+ 153. Kf5 Nh3 154. Ra2+ Kf3 155. Ra8 Nhf2 156. Re8 Nd1 157. Nd2+ Kf2 158. Ke4 Nc1 159. Nb1 Ke2 160. Kf4+ Kd3 161. Rd8+ Ke2 162. Rd2+ Ke1 163. Rh2 Ne2+ 164. Kf3 Nd4+ 165. Ke4 Nb3 166. Ra2 Nf2+ 167. Kf3 Nd4+ 168. Ke3 Nf5+ 169. Kf4 Nd4 170. Ra4 Nc2 171. Kf3 Nd3 172. Rh4 Kd1 173. Nc3+ Kd2 174. Ne4+ Kc1 175. Ke2 Ne5 176. Nc5 Na3 177. Re4 Nec4 178. Kd3 Nb2+ 179. Kc3 Nb1+ 180. Kd4 Na3 181. Rh4 Nb5+ 182. Ke5 Kc2 183. Rh2+ Kc3 184. Kd5 Nd1 185. Rh3+ Kb2 186. Nb7 Na3 187. Nd6 Nc3+ 188. Kc5 Kc2 189. Nf5 Nab1 190. Kd4 Nb5+ 191. Kc4 N5a3+ 192. Kc5 Kb2 193. Rh2+ Kb3 194. Nd4+ Kc3 195. Ne2+ Kb2 196. Ng3+ Kc3 197. Rh3 Kd3 198. Nf5+ Kc2 199. Rg3 Kb2 200. Ne3 Nd2 201. Rg2 Kc1 202. Kd4 Nf3+ 203. Kc3 Nb1+ 204. Kb4 Nbd2 205. Rg8 Ne4 206. Rd8 Nf2 207. Kc3 Ne4+ 208. Kd3 Nc5+ 209. Kc4 Ne4 210. Rd1+ Kb2 211. Rd5 Ne1 212. Rd8 Nf3 213. Rf8 Ne1 214. Rb8+ Kc1 215. Kd4 Nd2 216. Nd5 Kd1 217. Re8 Ng2 218. Kd3 Nb1 219. Re7 Ne1+ 220. Kc4 Ng2 221. Kb3 Nd2+ 222. Kb2 Nc4+ 223. Kc3 Nd2 224. Nf6 Nf4 225. Rd7 Ne2+ 226. Kd3 Nb1 227. Ke3+ Ke1 228. Re7 Kd1 229. Rh7 Nc1 230. Ne4 Na3 231. Nf2+ Kc2 232. Rc7+ Kb2 233. Nd1+ Kb1 234. Rc8 Nc2+ 235. Kd2 Nb3+ 236. Kd3 Ne1+ 237. Kc3 Kc1 238. Rd8 Nc5 239. Nf2 Na4+ 240. Kb3 Nb2 241. Rc8+ Kd2 242. Kxb2 Ke3 243. Ng4+ Kf4 244. Ne5 Ng2 245. Ng6+ Kg5 246. Rc3 Kg4 247. Rd3 Ne1 248. Rd4+ Kh5 249. Nh4 Nd3+ 250. Rxd3 [*]
http://kirill-kryukov.com/chess/longest-checkmates/longest-checkmates-sorted-by-length.shtml
